Pub Date : 2023-05-17DOI: 10.1080/00031305.2023.2242442
Quang Nguyen, Ronald Yurko, Gregory J. Matthews
In American football, a pass rush is an attempt by the defensive team to disrupt the offense and prevent the quarterback (QB) from completing a pass. Existing metrics for assessing pass rush performance are either discrete-time quantities or based on subjective judgment. Using player tracking data, we propose STRAIN, a novel metric for evaluating pass rushers in the National Football League (NFL) at the continuous-time within-play level. Inspired by the concept of strain rate in materials science, STRAIN is a simple and interpretable means for measuring defensive pressure in football. It is a directly-observed statistic as a function of two features: the distance between the pass rusher and QB, and the rate at which this distance is being reduced. Our metric possesses great predictability of pressure and stability over time. We also fit a multilevel model for STRAIN to understand the defensive pressure contribution of every pass rusher at the play-level. We apply our approach to NFL data and present results for the first eight weeks of the 2021 regular season. In particular, we provide comparisons of STRAIN for different defensive positions and play outcomes, and rankings of the NFL's best pass rushers according to our metric.
{"title":"Here Comes the STRAIN: Analyzing Defensive Pass Rush in American Football with Player Tracking Data","authors":"Quang Nguyen, Ronald Yurko, Gregory J. Matthews","doi":"10.1080/00031305.2023.2242442","DOIUrl":"https://doi.org/10.1080/00031305.2023.2242442","url":null,"abstract":"In American football, a pass rush is an attempt by the defensive team to disrupt the offense and prevent the quarterback (QB) from completing a pass. Existing metrics for assessing pass rush performance are either discrete-time quantities or based on subjective judgment. Using player tracking data, we propose STRAIN, a novel metric for evaluating pass rushers in the National Football League (NFL) at the continuous-time within-play level. Inspired by the concept of strain rate in materials science, STRAIN is a simple and interpretable means for measuring defensive pressure in football. It is a directly-observed statistic as a function of two features: the distance between the pass rusher and QB, and the rate at which this distance is being reduced. Our metric possesses great predictability of pressure and stability over time. We also fit a multilevel model for STRAIN to understand the defensive pressure contribution of every pass rusher at the play-level. We apply our approach to NFL data and present results for the first eight weeks of the 2021 regular season. In particular, we provide comparisons of STRAIN for different defensive positions and play outcomes, and rankings of the NFL's best pass rushers according to our metric.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129050616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-20DOI: 10.1080/00031305.2023.2205455
J. Bartroff, G. Lorden, Lijia Wang
We appreciate the recent paper of Schilling and Stanley (2022, hereafter SS) on confidence intervals for the hypergeometric being brought to our attention, which we were not aware of while preparing our paper (Bartroff, Lorden, and Wang 2022, hereafter BLW) on that subject. Although there are commonalities between the two approaches, there are some important distinctions that we highlight here. Following those papers’ notations, below we denote the confidence intervals for the hypergeometric success parameter based on sample size n and population size N by LCO for SS, and C∗ for BLW. In the numerical examples below, LCO (github.com/mfschilling/ HGCIs) and C∗ (github.com/bartroff792/hyper) were computed using the respective authors’ publicly available R code, running on the same computer. Computational time. LCO and C∗ differ drastically in the amount of time required to compute them. Figure 1 shows the computational time of LCO and C∗ for α = 0.05, N = 200, 400, . . . , 1000, and n = N/2. For example, for N = 1000 the computational time of LCO exceeds 100 min whereas C∗ requires roughly 1/10th of a second (0.002 min). In further numerical comparisons not included here, we found this relationship to be common for moderate to large values of the sample and population sizes, n and N. This may be due to the algorithm for computing LCO which calls for searching among all acceptance functions of minimal span (SS, p. 37). Provable optimality. SS contains two proofs, one in the Appendix of a basic result about the hypergeometric parameters, and one in the main text of the paper’s only theorem (SS, p. 33) which is a general result that size-optimal hypergeometric acceptance sets are inverted to yield size-optimal confidence “intervals.” However, not all inverted acceptance sets will yield proper intervals, and in practice one often ends up with noninterval confidence sets, for example, intervals with “gaps.” This occurs when the endpoint sequences of the acceptance intervals being inverted are non-monotonic, or themselves have gaps. SS address this by modifying their proposal in this situation to mimic a method of Schilling and Doi (2014) developed for the Binomial distribution. SS (pp. 36–37) write, Where there is a need to resolve a gap, in which case the minimal span acceptance function that causes the gap is replaced with the one having the
我们感谢最近Schilling和Stanley(2022，下文简称SS)关于超几何置信区间的论文引起了我们的注意，这是我们在准备关于该主题的论文(Bartroff, Lorden, and Wang 2022，下文简称BLW)时没有意识到的。尽管这两种方法之间存在共性，但我们在这里强调一些重要的区别。根据这些论文的注释，下面我们用LCO表示基于样本大小n和总体大小n的超几何成功参数的置信区间，LCO表示SS, C *表示BLW。在下面的数值示例中，LCO (github.com/mfschilling/ HGCIs)和C * (github.com/bartroff792/hyper)是使用各自作者在同一台计算机上运行的公开可用的R代码计算的。计算时间。LCO和C *在计算它们所需的时间上差别很大。图1显示了当α = 0.05, N = 200,400，…时LCO和C *的计算时间。， 1000, n = n /2。例如，当N = 1000时，LCO的计算时间超过100分钟，而C *大约需要1/10秒(0.002分钟)。在本文未包括的进一步数值比较中，我们发现这种关系对于样本和总体大小(n和n)的中大值是常见的。这可能是由于计算LCO的算法要求在最小跨度的所有可接受函数中进行搜索(SS，第37页)。可证明的最优。SS包含两个证明，一个在关于超几何参数的一个基本结果的附录中，另一个在本文唯一定理(SS，第33页)的正文中，该定理是大小最优的超几何可接受集被反转以产生大小最优的置信“区间”的一般结果。然而，并不是所有的反向接受集都会产生合适的区间，在实践中，人们经常会得到非区间置信集，例如，具有“间隙”的区间。当被反转的接受区间的端点序列是非单调的，或者其本身有间隙时，就会发生这种情况。SS通过修改他们在这种情况下的建议来解决这个问题，以模仿Schilling和Doi(2014)为二项分布开发的方法。SS(第36-37页)写道，当需要解决缺口时，在这种情况下，导致缺口的最小跨度接受函数被具有
{"title":"Response to Comment by Schilling","authors":"J. Bartroff, G. Lorden, Lijia Wang","doi":"10.1080/00031305.2023.2205455","DOIUrl":"https://doi.org/10.1080/00031305.2023.2205455","url":null,"abstract":"We appreciate the recent paper of Schilling and Stanley (2022, hereafter SS) on confidence intervals for the hypergeometric being brought to our attention, which we were not aware of while preparing our paper (Bartroff, Lorden, and Wang 2022, hereafter BLW) on that subject. Although there are commonalities between the two approaches, there are some important distinctions that we highlight here. Following those papers’ notations, below we denote the confidence intervals for the hypergeometric success parameter based on sample size n and population size N by LCO for SS, and C∗ for BLW. In the numerical examples below, LCO (github.com/mfschilling/ HGCIs) and C∗ (github.com/bartroff792/hyper) were computed using the respective authors’ publicly available R code, running on the same computer. Computational time. LCO and C∗ differ drastically in the amount of time required to compute them. Figure 1 shows the computational time of LCO and C∗ for α = 0.05, N = 200, 400, . . . , 1000, and n = N/2. For example, for N = 1000 the computational time of LCO exceeds 100 min whereas C∗ requires roughly 1/10th of a second (0.002 min). In further numerical comparisons not included here, we found this relationship to be common for moderate to large values of the sample and population sizes, n and N. This may be due to the algorithm for computing LCO which calls for searching among all acceptance functions of minimal span (SS, p. 37). Provable optimality. SS contains two proofs, one in the Appendix of a basic result about the hypergeometric parameters, and one in the main text of the paper’s only theorem (SS, p. 33) which is a general result that size-optimal hypergeometric acceptance sets are inverted to yield size-optimal confidence “intervals.” However, not all inverted acceptance sets will yield proper intervals, and in practice one often ends up with noninterval confidence sets, for example, intervals with “gaps.” This occurs when the endpoint sequences of the acceptance intervals being inverted are non-monotonic, or themselves have gaps. SS address this by modifying their proposal in this situation to mimic a method of Schilling and Doi (2014) developed for the Binomial distribution. SS (pp. 36–37) write, Where there is a need to resolve a gap, in which case the minimal span acceptance function that causes the gap is replaced with the one having the","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117097802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-11DOI: 10.1080/00031305.2023.2191670
Abstract Detecting change-points in multivariate settings is usually carried out by analyzing all marginals either independently, via univariate methods, or jointly, through multivariate approaches. The former discards any inherent dependencies between different marginals and the latter may suffer from domination/masking among different change-points of distinct marginals. As a remedy, we propose an approach which groups marginals with similar temporal behaviors, and then performs group-wise multivariate change-point detection. Our approach groups marginals based on hierarchical clustering using distances which adjust for inherent dependencies. Through a simulation study we show that our approach, by preventing domination/masking, significantly enhances the general performance of the employed multivariate change-point detection method. Finally, we apply our approach to two datasets: (i) Land Surface Temperature in Spain, during the years 2000–2021, and (ii) The WikiLeaks Afghan War Diary data.
{"title":"Hierarchical Spatio-Temporal Change-Point Detection","authors":"","doi":"10.1080/00031305.2023.2191670","DOIUrl":"https://doi.org/10.1080/00031305.2023.2191670","url":null,"abstract":"Abstract Detecting change-points in multivariate settings is usually carried out by analyzing all marginals either independently, via univariate methods, or jointly, through multivariate approaches. The former discards any inherent dependencies between different marginals and the latter may suffer from domination/masking among different change-points of distinct marginals. As a remedy, we propose an approach which groups marginals with similar temporal behaviors, and then performs group-wise multivariate change-point detection. Our approach groups marginals based on hierarchical clustering using distances which adjust for inherent dependencies. Through a simulation study we show that our approach, by preventing domination/masking, significantly enhances the general performance of the employed multivariate change-point detection method. Finally, we apply our approach to two datasets: (i) Land Surface Temperature in Spain, during the years 2000–2021, and (ii) The WikiLeaks Afghan War Diary data.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126166063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00031305.2023.2172078
K. Rice, T. Lumley
While we welcome Bower et al.’s (2022) exploration of how teaching need not rely on parametric methods alone, we wish to raise some issues with their presentation. First, “nonparametric”—meaning methods that do not rely on an assumed form of frequency distribution—is not synonymous with “rank-based.” When, as in Bower et al.’s (2022) examples, interest lies in differences in mean or median between groups, we could nonparametrically use permutation tests with test statistics that—straightforwardly—describe differences in sample mean or median between groups. These exact approaches use no assumptions other than independence of the outcomes (Berry, Johnston, and Mielke 2019, sec. 3.3) and that the test statistic being used captures deviations from the null that are of some scientific interest. So there is no need to switch to less-relevant rank-based methods, much less present them as the natural alternative to being parametric. We do agree with Bower et al. (2022) that user-friendly implementations are important, but permutation tests are available via simple R commands (e.g., the coin package’s oneway_test() function (Hothorn et al. 2008)) and shiny applications that are built on them. Second, the Kruskal-Wallis and Wilcoxon tests are not tests for population mean rank in the same sense that ANOVA and the t-test are tests for the mean, or Mood’s test is a test for the median. The issue is that the population mean and median for a subgroup are defined by the distribution of the response in just that subgroup. The mean rank, in contrast, depends on the distribution of responses in all subgroups and their sample sizes, so whether group 1 has higher mean rank than group 2 can depend on which other groups are also in the dataset. When the groups are not stochastically ordered, this leads to surprisingly complicated behavior of the Kruskal-Wallis test (Brown and Hettmansperger 2002). Finally, with regard to pedagogy we recommend the Data Problem-Solving Cycle (Wild and Pfannkuch 1999) in which the first step, “Problem,” identifies the question to address. This
虽然我们欢迎Bower等人(2022)对教学如何不需要单独依赖参数方法的探索，但我们希望对他们的陈述提出一些问题。首先，“非参数”——即不依赖于假设形式的频率分布的方法——与“基于秩的”不是同义词。在Bower等人(2022)的例子中，当兴趣在于组间均值或中位数的差异时，我们可以非参数地使用排列检验，其检验统计量可以直接描述组间样本均值或中位数的差异。这些精确的方法除了结果的独立性之外不使用任何假设(Berry, Johnston, and Mielke 2019，第3.3节)，并且所使用的检验统计量捕获了具有一定科学意义的零值偏差。因此，没有必要切换到不太相关的基于排名的方法，更不用说将它们作为参数化的自然替代方案了。我们确实同意Bower等人(2022)的观点，即用户友好的实现很重要，但排列测试可以通过简单的R命令(例如，coin包的oneway_test()函数(Hothorn等人，2008))和基于它们构建的光鲜的应用程序来实现。其次，Kruskal-Wallis和Wilcoxon检验不是总体平均秩的检验，而ANOVA和t检验是对平均值的检验，或者Mood检验是对中位数的检验。问题是，子组的总体均值和中位数是由该子组的响应分布定义的。相比之下，平均排名取决于所有子组中的响应分布及其样本量，因此，第一组的平均排名是否高于第二组，可能取决于数据集中还有哪些其他组。当群体不是随机排序时，这就导致了令人惊讶的复杂的Kruskal-Wallis测试行为(Brown and Hettmansperger 2002)。最后，关于教学法，我们推荐数据问题解决周期(Wild and Pfannkuch 1999)，其中第一步，“问题”，确定要解决的问题。这
{"title":"Comment on “A Case for Nonparametrics” by Bower et al.","authors":"K. Rice, T. Lumley","doi":"10.1080/00031305.2023.2172078","DOIUrl":"https://doi.org/10.1080/00031305.2023.2172078","url":null,"abstract":"While we welcome Bower et al.’s (2022) exploration of how teaching need not rely on parametric methods alone, we wish to raise some issues with their presentation. First, “nonparametric”—meaning methods that do not rely on an assumed form of frequency distribution—is not synonymous with “rank-based.” When, as in Bower et al.’s (2022) examples, interest lies in differences in mean or median between groups, we could nonparametrically use permutation tests with test statistics that—straightforwardly—describe differences in sample mean or median between groups. These exact approaches use no assumptions other than independence of the outcomes (Berry, Johnston, and Mielke 2019, sec. 3.3) and that the test statistic being used captures deviations from the null that are of some scientific interest. So there is no need to switch to less-relevant rank-based methods, much less present them as the natural alternative to being parametric. We do agree with Bower et al. (2022) that user-friendly implementations are important, but permutation tests are available via simple R commands (e.g., the coin package’s oneway_test() function (Hothorn et al. 2008)) and shiny applications that are built on them. Second, the Kruskal-Wallis and Wilcoxon tests are not tests for population mean rank in the same sense that ANOVA and the t-test are tests for the mean, or Mood’s test is a test for the median. The issue is that the population mean and median for a subgroup are defined by the distribution of the response in just that subgroup. The mean rank, in contrast, depends on the distribution of responses in all subgroups and their sample sizes, so whether group 1 has higher mean rank than group 2 can depend on which other groups are also in the dataset. When the groups are not stochastically ordered, this leads to surprisingly complicated behavior of the Kruskal-Wallis test (Brown and Hettmansperger 2002). Finally, with regard to pedagogy we recommend the Data Problem-Solving Cycle (Wild and Pfannkuch 1999) in which the first step, “Problem,” identifies the question to address. This","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131096062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00031305.2023.2182362
Roy Bower, William Cipolli
We recognize the careful reading of and thought-provoking commentary on our work by Rice and Lumley. Further, we appreciate the opportunity to respond and clarify our position regarding the three presented concerns. We address these points in three sections below and conclude with final remarks in Section 4.
{"title":"A Response to Rice and Lumley","authors":"Roy Bower, William Cipolli","doi":"10.1080/00031305.2023.2182362","DOIUrl":"https://doi.org/10.1080/00031305.2023.2182362","url":null,"abstract":"We recognize the careful reading of and thought-provoking commentary on our work by Rice and Lumley. Further, we appreciate the opportunity to respond and clarify our position regarding the three presented concerns. We address these points in three sections below and conclude with final remarks in Section 4.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132240624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00031305.2023.2197022
X. Puig, J. Ginebra
We use a Bayesian spatio-temporal model, first to smooth small-area initial life expectancy estimates in Barcelona for 2020, and second to predict what small-area life expectancy would have been in 2020 in absence of covid-19 using mortality data from 2007 to 2019. This allows us to estimate and map the small-area life expectancy loss, which can be used to assess how the impact of covid-19 varies spatially, and to explore whether that loss relates to underlying factors, such as population density, educational level, or proportion of older individuals living alone. We find that the small-area life expectancy loss for men and for women have similar distributions, and are spatially uncorrelated but positively correlated with population density and among themselves. On average, we estimate that the life expectancy loss in Barcelona in 2020 was of 2.01 years for men, falling back to 2011 levels, and of 2.11 years for women, falling back to 2006 levels.
{"title":"Mapping life expectancy loss in Barcelona in 2020","authors":"X. Puig, J. Ginebra","doi":"10.1080/00031305.2023.2197022","DOIUrl":"https://doi.org/10.1080/00031305.2023.2197022","url":null,"abstract":"We use a Bayesian spatio-temporal model, first to smooth small-area initial life expectancy estimates in Barcelona for 2020, and second to predict what small-area life expectancy would have been in 2020 in absence of covid-19 using mortality data from 2007 to 2019. This allows us to estimate and map the small-area life expectancy loss, which can be used to assess how the impact of covid-19 varies spatially, and to explore whether that loss relates to underlying factors, such as population density, educational level, or proportion of older individuals living alone. We find that the small-area life expectancy loss for men and for women have similar distributions, and are spatially uncorrelated but positively correlated with population density and among themselves. On average, we estimate that the life expectancy loss in Barcelona in 2020 was of 2.01 years for men, falling back to 2011 levels, and of 2.11 years for women, falling back to 2006 levels.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"537 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126128164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/00031305.2023.2198355
Junyong Park
Finite population sampling has found numerous applications in the past century. Validity inference of real populations is possible based on known sampling probabilities, “irrespectively of the unknown properties of the target population studied” (Neyman, 1934). Graphs allow one to incorporate the connections among the population units in addition. Many socio-economic, biological, spatial, or technological phenomena exhibit an underlying graph structure that may be the central interest of study, or the edges may effectively provide access to those nodes that are the primary targets. Either way, graph sampling provides a universally valid approach to studying realvalued graphs. This book establishes a rigorous conceptual framework for graph sampling and gives a unified presentation of much of the existing theory and methods, including several of the most recent developments. The most central concepts are introduced in Chapter 1, such as graph totals and parameters as targets of estimation, observation procedures following an initial sample of nodes that drive graph sampling, sample graph in which different kinds of induced subgraphs (such as edge, triangle, 4circle, K-star) can be observed, and graph sampling strategy consisting of a sampling method and an associated estimator. Chapters 2–4 introduce strategies based on bipartite graph sampling and incidence weighting estimator, which encompass all the existing unconventional finite population sampling methods, including indirect, network, adaptive cluster, or line intercept sampling. This can help to raise awareness of these methods, allowing them to be more effectively studied and applied as cases of graph sampling. For instance, Chapter 4 considers how to apply adaptive network sampling in a situation like the covid outbreak, which allows one to combat the virus spread by testtrace and to estimate the prevalence at the same time, provided the necessary elements of probability design and observation procedure are implemented. Chapters 5 and 6 deal with snowball sampling and targeted random walk sampling, respectively, which can be regarded as probabilistic breath-first or depth-first non-exhaustive search methods in graphs. Novel approaches to sampling strategies are developed and illustrated, such as how to account for the fact that an observed triangle could have been observed in many other ways that remain hidden from the realized sample graph, or how to estimate a parameter related to certain finiteorder subgraphs (such as a triangle) based on a random walk in the graph. The Bibliographic Notes at the end of each chapter contain some reflections on sources of inspiration, motivations for chosen approaches, and topics for future development. I found that the contents of the book are highly innovative and useful. The indirect sampling of Lavillee (2007) can be viewed as a special case of graph sampling. The materials in adaptive cluster sampling should be very useful in many real-world sampling
{"title":"Handbook of Multiple Comparisons","authors":"Junyong Park","doi":"10.1080/00031305.2023.2198355","DOIUrl":"https://doi.org/10.1080/00031305.2023.2198355","url":null,"abstract":"Finite population sampling has found numerous applications in the past century. Validity inference of real populations is possible based on known sampling probabilities, “irrespectively of the unknown properties of the target population studied” (Neyman, 1934). Graphs allow one to incorporate the connections among the population units in addition. Many socio-economic, biological, spatial, or technological phenomena exhibit an underlying graph structure that may be the central interest of study, or the edges may effectively provide access to those nodes that are the primary targets. Either way, graph sampling provides a universally valid approach to studying realvalued graphs. This book establishes a rigorous conceptual framework for graph sampling and gives a unified presentation of much of the existing theory and methods, including several of the most recent developments. The most central concepts are introduced in Chapter 1, such as graph totals and parameters as targets of estimation, observation procedures following an initial sample of nodes that drive graph sampling, sample graph in which different kinds of induced subgraphs (such as edge, triangle, 4circle, K-star) can be observed, and graph sampling strategy consisting of a sampling method and an associated estimator. Chapters 2–4 introduce strategies based on bipartite graph sampling and incidence weighting estimator, which encompass all the existing unconventional finite population sampling methods, including indirect, network, adaptive cluster, or line intercept sampling. This can help to raise awareness of these methods, allowing them to be more effectively studied and applied as cases of graph sampling. For instance, Chapter 4 considers how to apply adaptive network sampling in a situation like the covid outbreak, which allows one to combat the virus spread by testtrace and to estimate the prevalence at the same time, provided the necessary elements of probability design and observation procedure are implemented. Chapters 5 and 6 deal with snowball sampling and targeted random walk sampling, respectively, which can be regarded as probabilistic breath-first or depth-first non-exhaustive search methods in graphs. Novel approaches to sampling strategies are developed and illustrated, such as how to account for the fact that an observed triangle could have been observed in many other ways that remain hidden from the realized sample graph, or how to estimate a parameter related to certain finiteorder subgraphs (such as a triangle) based on a random walk in the graph. The Bibliographic Notes at the end of each chapter contain some reflections on sources of inspiration, motivations for chosen approaches, and topics for future development. I found that the contents of the book are highly innovative and useful. The indirect sampling of Lavillee (2007) can be viewed as a special case of graph sampling. The materials in adaptive cluster sampling should be very useful in many real-world sampling","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127908484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-30DOI: 10.1080/00031305.2023.2197021
M. Schilling
The article “Optimal and Fast Confidence Intervals for Hypergeometric Successes” by Bartroff, J., Lorden, G. and Wang, L. (BLW) develops a procedure for interval estimation of the number of successes M in a finite population based on constructing minimal length symmetrical acceptance intervals, which are inverted to determine confidence intervals based on the number of successes x obtained from a sample of size n. The authors compare their procedure to previously developed methods derived from the method of pivoting (Buonaccorsi 1987; Konijn 1973; Casella and Berger 2002, chap. 9) as well as to the more recent work of Wang (2015), and show that their approach generally leads to substantially shorter confidence intervals than those of these competitors, while frequently achieving higher coverage. However, the present authors BLW were evidently unaware of my recent paper with A. Stanley, “A New Approach to Precise Interval Estimation for the Parameters of the Hypergeometric Distribution” (Schilling and Stanley 2020), which solved the problem of constructing a hypergeometric confidence procedure that has minimal length (that is, minimal total cardinality of the confidence intervals for x = 0 to n), while maximizing coverage among all length minimizing procedures. We also compared our method to the same competitors as those listed above, as well as to one that can be obtained from Blaker’s (2000) method, and we showed the superiority in performance of our procedure. The two goals of our paper—length minimization and maximal coverage—are the same as those in BLW’s paper, and BLW’s approach matches rather closely with ours. The authors’ “α optimal” is our “minimal cardinality,” while our “maximal coverage” is BLW’s “PM-maximizing.” The only substantive difference between the two confidence procedures is that BLW’s specifies symmetrical acceptance sets, while ours does not. This affects only a small number of confidence intervals. An investigation of all 95% confidence intervals for each population size N between 5 and 100 and sample sizes n = 5, 10, . . . with n ≤ N finds that BLW’s confidence intervals are identical to ours in 99.43% of the 34,200 intervals checked. When they are different, the BLW
{"title":"Bartroff, J., Lorden, G. and Wang, L. (2022), “Optimal and Fast Confidence Intervals for Hypergeometric Successes,” The American Statistician: Comment by Schilling","authors":"M. Schilling","doi":"10.1080/00031305.2023.2197021","DOIUrl":"https://doi.org/10.1080/00031305.2023.2197021","url":null,"abstract":"The article “Optimal and Fast Confidence Intervals for Hypergeometric Successes” by Bartroff, J., Lorden, G. and Wang, L. (BLW) develops a procedure for interval estimation of the number of successes M in a finite population based on constructing minimal length symmetrical acceptance intervals, which are inverted to determine confidence intervals based on the number of successes x obtained from a sample of size n. The authors compare their procedure to previously developed methods derived from the method of pivoting (Buonaccorsi 1987; Konijn 1973; Casella and Berger 2002, chap. 9) as well as to the more recent work of Wang (2015), and show that their approach generally leads to substantially shorter confidence intervals than those of these competitors, while frequently achieving higher coverage. However, the present authors BLW were evidently unaware of my recent paper with A. Stanley, “A New Approach to Precise Interval Estimation for the Parameters of the Hypergeometric Distribution” (Schilling and Stanley 2020), which solved the problem of constructing a hypergeometric confidence procedure that has minimal length (that is, minimal total cardinality of the confidence intervals for x = 0 to n), while maximizing coverage among all length minimizing procedures. We also compared our method to the same competitors as those listed above, as well as to one that can be obtained from Blaker’s (2000) method, and we showed the superiority in performance of our procedure. The two goals of our paper—length minimization and maximal coverage—are the same as those in BLW’s paper, and BLW’s approach matches rather closely with ours. The authors’ “α optimal” is our “minimal cardinality,” while our “maximal coverage” is BLW’s “PM-maximizing.” The only substantive difference between the two confidence procedures is that BLW’s specifies symmetrical acceptance sets, while ours does not. This affects only a small number of confidence intervals. An investigation of all 95% confidence intervals for each population size N between 5 and 100 and sample sizes n = 5, 10, . . . with n ≤ N finds that BLW’s confidence intervals are identical to ours in 99.43% of the 34,200 intervals checked. When they are different, the BLW","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132865500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-27DOI: 10.1080/00031305.2023.2184423
The author presented a proof that a regression estimator unbiased for all distributions in a sufficiently broad family F0 must be linear. The family was taken to consist of the convolutions of all two-point distributions with a scale-family of smooth densities tending to a point mass at zero. The basic calculations were based solely on the discrete distributions, but the convolutions were introduced so that the family would be a subset of some standard, smooth nonparametric families. For example, adaptive estimation requires enough smoothness so that the Cramér-Rao bound provides optimal asymptotics. Some further comments appear in the supplemental material. The proof required that convergence of the smooth densities to zero implied that the expectations under the smooth convolutions converged to the expectation under the two-point distribution. This requires that the estimate be continuous, and there was a major error in the proof that unbiasedness implies continuity. It appears that continuity cannot be proved using unbiasedness over F0 , but it can be proved using unbiasedness over families of discrete distributions (see supplemental material). Thus, either the estimator must be assumed to be continuous, or a result using only discrete distributions is required. In trying to correct the error, a much simpler proof of the linearity result was found. This proof takes F0 to consist only of discrete distributions. The details are also presented in the supplemental material, but the basic idea is relatively simple: Consider a simplex with center at zero. Each point in the simplex (say −y ) is a convex combination of the vertices of the simplex; that is, −y is the expectation for a (discrete) distribution putting probability pi on vertex zi . Thus, the distribution putting probability 2 on y and 1 2 pi on zi has mean zero. Therefore, by unbiasedness, T(y) is a convex combination of the {T(zi)} ; that is, T(y) is the matrix whose columns are T(zi) times a vector, p , of probabilities. By basic properties of a simplex, p is an affine function of −y ; and so T(y) is an affine function of y . By unbiasedness under a point mass at zero, T(0) = 0 ; and so the affine constant is zero and T must be linear.
{"title":"Correction: Linearity of Unbiased Linear Model Estimators","authors":"","doi":"10.1080/00031305.2023.2184423","DOIUrl":"https://doi.org/10.1080/00031305.2023.2184423","url":null,"abstract":"The author presented a proof that a regression estimator unbiased for all distributions in a sufficiently broad family F0 must be linear. The family was taken to consist of the convolutions of all two-point distributions with a scale-family of smooth densities tending to a point mass at zero. The basic calculations were based solely on the discrete distributions, but the convolutions were introduced so that the family would be a subset of some standard, smooth nonparametric families. For example, adaptive estimation requires enough smoothness so that the Cramér-Rao bound provides optimal asymptotics. Some further comments appear in the supplemental material. The proof required that convergence of the smooth densities to zero implied that the expectations under the smooth convolutions converged to the expectation under the two-point distribution. This requires that the estimate be continuous, and there was a major error in the proof that unbiasedness implies continuity. It appears that continuity cannot be proved using unbiasedness over F0 , but it can be proved using unbiasedness over families of discrete distributions (see supplemental material). Thus, either the estimator must be assumed to be continuous, or a result using only discrete distributions is required. In trying to correct the error, a much simpler proof of the linearity result was found. This proof takes F0 to consist only of discrete distributions. The details are also presented in the supplemental material, but the basic idea is relatively simple: Consider a simplex with center at zero. Each point in the simplex (say −y ) is a convex combination of the vertices of the simplex; that is, −y is the expectation for a (discrete) distribution putting probability pi on vertex zi . Thus, the distribution putting probability 2 on y and 1 2 pi on zi has mean zero. Therefore, by unbiasedness, T(y) is a convex combination of the {T(zi)} ; that is, T(y) is the matrix whose columns are T(zi) times a vector, p , of probabilities. By basic properties of a simplex, p is an affine function of −y ; and so T(y) is an affine function of y . By unbiasedness under a point mass at zero, T(0) = 0 ; and so the affine constant is zero and T must be linear.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123041885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：