Adversarial Risk Analysis (ARA) can be a more realistic and practical alternative to traditional game theoretic or decision theoretic approaches for modeling strategic decision‐making in the presence of an adversary. ARA relies on quantifying the decision‐maker's (DM's) uncertainties about the adversary's strategic thinking, choices and utilities via probability distributions to identify the optimal solution for the DM. ARA solution will be sensitive to the choices of prior distributions used for modelling the expert beliefs. Yet, to date, no mathematical results to characterize the robustness of the ARA solution to the misspecification of one or more prior distributions exist. Prior elicitation is known to be challenging. We present the very first mathematical results on the global robustness of the ARA solution. We use the distorted band class of priors and establish the conditions under which an ordering on the ARA solution can be established when modelling the first‐price sealed‐bid auctions using the nonstrategic play and level‐ thinking solution concepts. We illustrate these results using numerical examples and discuss further areas of research.
与传统的博弈论或决策论方法相比，对抗性风险分析（ARA）是一种更现实、更实用的方法，可用于在有对手的情况下建立战略决策模型。对抗风险分析依赖于通过概率分布量化决策者（DM）对对手战略思维、选择和效用的不确定性，从而为决策者确定最优解。ARA 解决方案对用于模拟专家信念的先验分布的选择非常敏感。然而，迄今为止，还没有任何数学结果可以描述 ARA 解决方案对一个或多个先验分布的错误指定的鲁棒性。众所周知，先验激发具有挑战性。我们首次提出了 ARA 解决方案全局鲁棒性的数学结果。我们使用了扭曲带类先验，并建立了一些条件，在这些条件下，使用非战略博弈和水平思维解决方案概念对第一价格密封出价拍卖进行建模时，可以建立 ARA 解决方案的排序。我们用数字示例说明了这些结果，并讨论了进一步的研究领域。
{"title":"On global robustness of an adversarial risk analysis solution","authors":"Jinming Yang, Chaitanya Joshi, Fabrizio Ruggeri","doi":"10.1111/stan.12361","DOIUrl":"https://doi.org/10.1111/stan.12361","url":null,"abstract":"Adversarial Risk Analysis (ARA) can be a more realistic and practical alternative to traditional game theoretic or decision theoretic approaches for modeling strategic decision‐making in the presence of an adversary. ARA relies on quantifying the decision‐maker's (DM's) uncertainties about the adversary's strategic thinking, choices and utilities via probability distributions to identify the optimal solution for the DM. ARA solution will be sensitive to the choices of prior distributions used for modelling the expert beliefs. Yet, to date, no mathematical results to characterize the robustness of the ARA solution to the misspecification of one or more prior distributions exist. Prior elicitation is known to be challenging. We present the very first mathematical results on the global robustness of the ARA solution. We use the distorted band class of priors and establish the conditions under which an ordering on the ARA solution can be established when modelling the first‐price sealed‐bid auctions using the <jats:italic>nonstrategic play</jats:italic> and <jats:italic>level‐</jats:italic> thinking solution concepts. We illustrate these results using numerical examples and discuss further areas of research.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of testing the existence of a heterogeneous dense subhypergraph. The null hypothesis corresponds to a heterogeneous Erdös–Rényi uniform random hypergraph and the alternative hypothesis corresponds to a heterogeneous uniform random hypergraph that contains a dense subhypergraph. We establish detection boundaries when the edge probabilities are known and construct an asymptotically powerful test for distinguishing the hypotheses. We also construct an adaptive test which does not involve edge probabilities, and hence, is more practically useful.
{"title":"Heterogeneous dense subhypergraph detection","authors":"Mingao Yuan, Zuofeng Shang","doi":"10.1111/stan.12360","DOIUrl":"https://doi.org/10.1111/stan.12360","url":null,"abstract":"We study the problem of testing the existence of a heterogeneous dense subhypergraph. The null hypothesis corresponds to a heterogeneous Erdös–Rényi uniform random hypergraph and the alternative hypothesis corresponds to a heterogeneous uniform random hypergraph that contains a dense subhypergraph. We establish detection boundaries when the edge probabilities are known and construct an asymptotically powerful test for distinguishing the hypotheses. We also construct an adaptive test which does not involve edge probabilities, and hence, is more practically useful.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ansgar Steland, Ewaryst Rafajłowicz, Wojciech Rafajłowicz
Having in mind applications in statistics and machine learning such as individualized care monitoring, or watermark detection in large language models, we consider the following general setting: When monitoring a sequence of observations, , there may be additional information, , on the environment which should be used to design the monitoring procedure. This additional information can be incorporated by applying threshold functions to the standardized measurements to adapt the detector to the environment. For the case of categorical data encoding of discrete‐valued environmental information we study several classes of level threshold functions including a proportional one which favors rare events among imbalanced classes. For the latter rule asymptotic theory is developed for independent and identically distributed and dependent learning samples including data from new discrete autoregressive moving average model (NDARMA) series and Hidden Markov Models. Further, we propose two‐stage designs which allow to distribute in a controlled way the budget over an a priori partition of the sample space of . The approach is illustrated by a real medical data set.
{"title":"General adapted‐threshold monitoring in discrete environments and rules for imbalanced classes","authors":"Ansgar Steland, Ewaryst Rafajłowicz, Wojciech Rafajłowicz","doi":"10.1111/stan.12352","DOIUrl":"https://doi.org/10.1111/stan.12352","url":null,"abstract":"Having in mind applications in statistics and machine learning such as individualized care monitoring, or watermark detection in large language models, we consider the following general setting: When monitoring a sequence of observations, , there may be additional information, , on the environment which should be used to design the monitoring procedure. This additional information can be incorporated by applying threshold functions to the standardized measurements to adapt the detector to the environment. For the case of categorical data encoding of discrete‐valued environmental information we study several classes of level threshold functions including a proportional one which favors rare events among imbalanced classes. For the latter rule asymptotic theory is developed for independent and identically distributed and dependent learning samples including data from new discrete autoregressive moving average model (NDARMA) series and Hidden Markov Models. Further, we propose two‐stage designs which allow to distribute in a controlled way the budget over an a priori partition of the sample space of . The approach is illustrated by a real medical data set.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rebecca Marion, Johannes Lederer, Bernadette Goevarts, Rainer von Sachs
Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g., highly correlated groups of variables). To improve prediction accuracy, various methods have been proposed to identify variable clusters from the data and integrate cluster information into a sparse modeling process. But none of these methods achieve satisfactory performance for prediction, variable selection and variable clustering performed simultaneously. This paper presents Variable Cluster Principal Component Regression (VC‐PCR), a prediction method that uses variable selection and variable clustering in order to solve this problem. Experiments with real and simulated data demonstrate that, compared to competitor methods, VC‐PCR is the only method that achieves simultaneously good prediction, variable selection, and clustering performance when cluster structure is present.
{"title":"VC‐PCR: A prediction method based on variable selection and clustering","authors":"Rebecca Marion, Johannes Lederer, Bernadette Goevarts, Rainer von Sachs","doi":"10.1111/stan.12358","DOIUrl":"https://doi.org/10.1111/stan.12358","url":null,"abstract":"Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g., highly correlated groups of variables). To improve prediction accuracy, various methods have been proposed to identify variable clusters from the data and integrate cluster information into a sparse modeling process. But none of these methods achieve satisfactory performance for prediction, variable selection and variable clustering performed simultaneously. This paper presents Variable Cluster Principal Component Regression (VC‐PCR), a prediction method that uses variable selection and variable clustering in order to solve this problem. Experiments with real and simulated data demonstrate that, compared to competitor methods, VC‐PCR is the only method that achieves simultaneously good prediction, variable selection, and clustering performance when cluster structure is present.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In density estimation, the mean integrated squared error (MISE) is commonly used as a measure of performance. In that setting, the cross‐validation criterion provides an unbiased estimator of the MISE minus the integral of the squared density. Since the minimum MISE is known to converge to zero, this suggests that the minimum value of the cross‐validation criterion could be regarded as an estimator of minus the integrated squared density. This novel proposal presents the outstanding feature that, unlike all other existing estimators, it does not need the choice of any tuning parameter. Indeed, it is proved here that this approach results in a consistent and efficient estimator, with remarkable performance in practice. Moreover, apart from this base case, it is shown how several other problems on density functional estimation can be similarly handled using this new principle, thus demonstrating full potential for further applications.
在密度估计中，通常使用平均综合平方误差（MISE）来衡量性能。在这种情况下，交叉验证准则提供了 MISE 减去密度平方积分的无偏估计值。由于已知最小 MISE 趋于零，这表明交叉验证准则的最小值可被视为减去平方密度积分的估计值。与其他所有现有估计器不同的是，这一新颖的建议具有无需选择任何调整参数的突出特点。事实上，本文证明了这种方法能产生一致且高效的估计器，并在实践中表现出卓越的性能。此外，除了这个基本案例，本文还展示了如何利用这一新原理同样处理其他几个关于密度函数估计的问题，从而充分展示了进一步应用的潜力。
{"title":"Estimation of density functionals via cross‐validation","authors":"José E. Chacón, Carlos Tenreiro","doi":"10.1111/stan.12359","DOIUrl":"https://doi.org/10.1111/stan.12359","url":null,"abstract":"In density estimation, the mean integrated squared error (MISE) is commonly used as a measure of performance. In that setting, the cross‐validation criterion provides an unbiased estimator of the MISE minus the integral of the squared density. Since the minimum MISE is known to converge to zero, this suggests that the minimum value of the cross‐validation criterion could be regarded as an estimator of minus the integrated squared density. This novel proposal presents the outstanding feature that, unlike all other existing estimators, it does not need the choice of any tuning parameter. Indeed, it is proved here that this approach results in a consistent and efficient estimator, with remarkable performance in practice. Moreover, apart from this base case, it is shown how several other problems on density functional estimation can be similarly handled using this new principle, thus demonstrating full potential for further applications.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces an artificial neural network (ANN) approach to estimate the autoregressive process AR(1) when the autocorrelation parameter is near one. Traditional ordinary least squares (OLS) estimators suffer from biases in small samples, necessitating various correction methods proposed in the literature. The ANN, trained on simulated data, outperforms these methods due to its nonlinear structure. Unlike competitors requiring simulations for bias corrections based on specific sample sizes, the ANN directly incorporates sample size as input, eliminating the need for repeated simulations. Stability tests involve exploring different ANN architectures and activation functions and robustness to varying distributions of the process innovations. Empirical applications on financial and industrial data highlight significant differences among methods, with ANN estimates suggesting lower persistence than other approaches.
本文介绍了一种人工神经网络（ANN）方法，用于估计自相关参数接近 1 时的自回归过程 AR(1)。传统的普通最小二乘法（OLS）估计器在小样本时存在偏差，因此需要采用文献中提出的各种修正方法。在模拟数据基础上训练的方差网络因其非线性结构而优于这些方法。与需要根据特定样本大小进行模拟以纠正偏差的竞争对手不同，方差网络直接将样本大小作为输入，无需重复模拟。稳定性测试包括探索不同的 ANN 架构和激活函数，以及对过程创新的不同分布的稳健性。金融和工业数据的实证应用凸显了各种方法之间的显著差异，其中方差网络估算的持久性低于其他方法。
{"title":"Artificial neural network small‐sample‐bias‐corrections of the AR(1) parameter close to unit root","authors":"Haozhe Jiang, Ostap Okhrin, Michael Rockinger","doi":"10.1111/stan.12354","DOIUrl":"https://doi.org/10.1111/stan.12354","url":null,"abstract":"This paper introduces an artificial neural network (ANN) approach to estimate the autoregressive process AR(1) when the autocorrelation parameter is near one. Traditional ordinary least squares (OLS) estimators suffer from biases in small samples, necessitating various correction methods proposed in the literature. The ANN, trained on simulated data, outperforms these methods due to its nonlinear structure. Unlike competitors requiring simulations for bias corrections based on specific sample sizes, the ANN directly incorporates sample size as input, eliminating the need for repeated simulations. Stability tests involve exploring different ANN architectures and activation functions and robustness to varying distributions of the process innovations. Empirical applications on financial and industrial data highlight significant differences among methods, with ANN estimates suggesting lower persistence than other approaches.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Subhankar Dutta, Hon Keung Tony Ng, Suchandan Kayal
In this study, statistical inference for competing risks model with latent failure times following the Kumaraswamy‐G (Kw‐G) family of distributions under a unified progressive hybrid censoring (UPHC) scheme is developed. Maximum likelihood estimates (MLEs) of the unknown model parameters are obtained, and their existence and uniqueness properties are discussed. Using the asymptotic properties of MLEs, the approximate confidence intervals for the model parameters are constructed. Further, Bayes estimates with associated highest posterior density credible intervals for the model parameters are developed under squared error loss function with informative and noninformative priors. These estimates are obtained under both restricted and nonrestricted parameter spaces. Moreover, frequentist and Bayesian approaches are developed to test the equality of shape parameters of the two competing failure causes. The comparison of censoring schemes based on different criteria is also discussed. Monte Carlo simulation studies are used to evaluate the performance of the proposed statistical inference procedures. An electrical appliances data set is analyzed to illustrate the applicability of the proposed methodologies.
{"title":"Inference for Kumaraswamy‐G family of distributions under unified progressive hybrid censoring with partially observed competing risks data","authors":"Subhankar Dutta, Hon Keung Tony Ng, Suchandan Kayal","doi":"10.1111/stan.12357","DOIUrl":"https://doi.org/10.1111/stan.12357","url":null,"abstract":"In this study, statistical inference for competing risks model with latent failure times following the Kumaraswamy‐G (Kw‐G) family of distributions under a unified progressive hybrid censoring (UPHC) scheme is developed. Maximum likelihood estimates (MLEs) of the unknown model parameters are obtained, and their existence and uniqueness properties are discussed. Using the asymptotic properties of MLEs, the approximate confidence intervals for the model parameters are constructed. Further, Bayes estimates with associated highest posterior density credible intervals for the model parameters are developed under squared error loss function with informative and noninformative priors. These estimates are obtained under both restricted and nonrestricted parameter spaces. Moreover, frequentist and Bayesian approaches are developed to test the equality of shape parameters of the two competing failure causes. The comparison of censoring schemes based on different criteria is also discussed. Monte Carlo simulation studies are used to evaluate the performance of the proposed statistical inference procedures. An electrical appliances data set is analyzed to illustrate the applicability of the proposed methodologies.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The subject of this work is the allocation of trials to subregions in crop variety testing in the case of correlated genotype effects. A solution for computation of optimal allocations using the OptimalDesign package in R is proposed. The obtained optimal designs minimize linear criteria based on the mean squared error matrix of the best linear unbiased prediction of the genotype effects. The proposed computational approach allows for any kind of additional linear constraint on the designs. The results are illustrated by a real data example.
这项工作的主题是在基因型效应相关的情况下，如何在作物品种测试中将试验分配到子区域。本文提出了一种使用 R 软件包 OptimalDesign 计算最优分配的解决方案。根据基因型效应的最佳线性无偏预测的均方误差矩阵，所获得的最优设计能最大限度地降低线性标准。所提出的计算方法允许对设计进行任何额外的线性约束。一个真实数据实例对结果进行了说明。
{"title":"Computing optimal allocation of trials to subregions in crop‐variety testing in case of correlated genotype effects","authors":"Maryna Prus","doi":"10.1111/stan.12353","DOIUrl":"https://doi.org/10.1111/stan.12353","url":null,"abstract":"The subject of this work is the allocation of trials to subregions in crop variety testing in the case of correlated genotype effects. A solution for computation of optimal allocations using the OptimalDesign package in R is proposed. The obtained optimal designs minimize linear criteria based on the mean squared error matrix of the best linear unbiased prediction of the genotype effects. The proposed computational approach allows for any kind of additional linear constraint on the designs. The results are illustrated by a real data example.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log‐log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf‐polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.
{"title":"Degree distributions in networks: Beyond the power law","authors":"Clement Lee, Emma F. Eastoe, Aiden Farrell","doi":"10.1111/stan.12355","DOIUrl":"https://doi.org/10.1111/stan.12355","url":null,"abstract":"The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log‐log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf‐polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, nonresponse rates in sample surveys have been increasing. Nonresponse bias is a serious concern in the analysis of sample surveys. The calibration and propensity score methods are used to adjust nonresponse bias. The propensity score method uses the weights of the inverse probability of response. The inverse probability of response is estimated by the auxiliary variables observed in respondents and nonrespondents. The calibration method can use additional auxiliary variables observed only in respondents if the population distributions of the variables are known. The calibration method is widely used; however, the theoretical property in the nonresponse situation has not been investigated. This study provides a condition that the calibration weights asymptotically go to the inverse probability of response and clarifies the relationship between the calibration and propensity score methods.
{"title":"A note on convergence of calibration weights to inverse probability weights","authors":"Tadayoshi Fushiki","doi":"10.1111/stan.12356","DOIUrl":"https://doi.org/10.1111/stan.12356","url":null,"abstract":"Recently, nonresponse rates in sample surveys have been increasing. Nonresponse bias is a serious concern in the analysis of sample surveys. The calibration and propensity score methods are used to adjust nonresponse bias. The propensity score method uses the weights of the inverse probability of response. The inverse probability of response is estimated by the auxiliary variables observed in respondents and nonrespondents. The calibration method can use additional auxiliary variables observed only in respondents if the population distributions of the variables are known. The calibration method is widely used; however, the theoretical property in the nonresponse situation has not been investigated. This study provides a condition that the calibration weights asymptotically go to the inverse probability of response and clarifies the relationship between the calibration and propensity score methods.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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