{"title":"A special section honoring Nils Lid Hjort","authors":"Ørnulf Borgan, Ingrid K. Glad","doi":"10.1111/sjos.12745","DOIUrl":"https://doi.org/10.1111/sjos.12745","url":null,"abstract":"","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"126 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141780376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Georgios Aristotelous, Theodore Kypraios, Philip D. O'Neill
This paper addresses the problem of assessing the homogeneity of the disease transmission process in stochastic epidemic models in populations that are partitioned into social groups. We develop a classical hypothesis test for completed epidemics which assesses whether or not there is significant within‐group transmission during an outbreak. The test is based on time‐ordered group labels of individuals. The null hypothesis is that of homogeneity of disease transmission among individuals, a hypothesis under which the discrete random vector of groups labels has a known sampling distribution that is independent of any model parameters. The test exhibits excellent performance when applied to various scenarios of simulated data and is also illustrated using two real‐life epidemic data sets. We develop some asymptotic theory including a central limit theorem. The test is practically very appealing, being computationally cheap and straightforward to implement, as well as being applicable to a wide range of real‐life outbreak settings and to related problems in other fields.
{"title":"A classical hypothesis test for assessing the homogeneity of disease transmission in stochastic epidemic models","authors":"Georgios Aristotelous, Theodore Kypraios, Philip D. O'Neill","doi":"10.1111/sjos.12743","DOIUrl":"https://doi.org/10.1111/sjos.12743","url":null,"abstract":"This paper addresses the problem of assessing the homogeneity of the disease transmission process in stochastic epidemic models in populations that are partitioned into social groups. We develop a classical hypothesis test for completed epidemics which assesses whether or not there is significant within‐group transmission during an outbreak. The test is based on time‐ordered group labels of individuals. The null hypothesis is that of homogeneity of disease transmission among individuals, a hypothesis under which the discrete random vector of groups labels has a known sampling distribution that is independent of any model parameters. The test exhibits excellent performance when applied to various scenarios of simulated data and is also illustrated using two real‐life epidemic data sets. We develop some asymptotic theory including a central limit theorem. The test is practically very appealing, being computationally cheap and straightforward to implement, as well as being applicable to a wide range of real‐life outbreak settings and to related problems in other fields.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"61 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the nonparametric estimation for the density of the stationary distribution of a ‐dimensional stochastic differential equation . From the continuous observation of the sampling path on , we study the estimation of as goes to infinity. For , we characterize the minimax rate for the ‐risk in pointwise estimation over a class of anisotropic Hölder functions with regularity . For , our finding is that, having ordered the smoothness such that , the minimax rate depends on whether or . In the first case, this rate is , and in the second case, it is , where is an explicit exponent dependent on the dimension and , the harmonic mean of smoothness over the directions after excluding and , the smallest ones. We also demonstrate that kernel‐based estimators achieve the optimal minimax rate. Furthermore, we propose an adaptive procedure for both integrated and pointwise risk. In the two‐dimensional case, we show that kernel density estimators achieve the rate , which is optimal in the minimax sense. Finally we illustrate the validity of our theoretical findings by proposing numerical results.
{"title":"Minimax rate of estimation for invariant densities associated to continuous stochastic differential equations over anisotropic Hölder classes","authors":"Chiara Amorino, Arnaud Gloter","doi":"10.1111/sjos.12735","DOIUrl":"https://doi.org/10.1111/sjos.12735","url":null,"abstract":"We study the problem of the nonparametric estimation for the density of the stationary distribution of a ‐dimensional stochastic differential equation . From the continuous observation of the sampling path on , we study the estimation of as goes to infinity. For , we characterize the minimax rate for the ‐risk in pointwise estimation over a class of anisotropic Hölder functions with regularity . For , our finding is that, having ordered the smoothness such that , the minimax rate depends on whether or . In the first case, this rate is , and in the second case, it is , where is an explicit exponent dependent on the dimension and , the harmonic mean of smoothness over the directions after excluding and , the smallest ones. We also demonstrate that kernel‐based estimators achieve the optimal minimax rate. Furthermore, we propose an adaptive procedure for both integrated and pointwise risk. In the two‐dimensional case, we show that kernel density estimators achieve the rate , which is optimal in the minimax sense. Finally we illustrate the validity of our theoretical findings by proposing numerical results.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"32 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The win ratio has in the recent decade gained popularity for analyzing prioritized multiple event data in clinical cohort studies, in particular within cardiovascular research. The literature on estimation of the win ratio using censored event data is however sparse. The methods that have been suggested have either an insufficient adjustment of the censoring or by assuming the the win and loss probabilities are proportional over time. The assumption of proportional win and loss probabilities will often in practice not be satisfied. In this paper, we present estimates for the win ratio, and win and loss probabilities, under independent right‐censoring and derive the asymptotic distribution of the estimates. The proposed win ratio estimate does not require the assumption of proportional win and loss probabilities. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on two data sets.
{"title":"Estimation of win, loss probabilities, and win ratio based on right‐censored event data","authors":"Erik T. Parner, Morten Overgaard","doi":"10.1111/sjos.12734","DOIUrl":"https://doi.org/10.1111/sjos.12734","url":null,"abstract":"The win ratio has in the recent decade gained popularity for analyzing prioritized multiple event data in clinical cohort studies, in particular within cardiovascular research. The literature on estimation of the win ratio using censored event data is however sparse. The methods that have been suggested have either an insufficient adjustment of the censoring or by assuming the the win and loss probabilities are proportional over time. The assumption of proportional win and loss probabilities will often in practice not be satisfied. In this paper, we present estimates for the win ratio, and win and loss probabilities, under independent right‐censoring and derive the asymptotic distribution of the estimates. The proposed win ratio estimate does not require the assumption of proportional win and loss probabilities. The small sample properties of the proposed method are studied in a simulation study showing that the variance formula is accurate even for small samples. The method is applied on two data sets.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Commentary on “Pitfalls of amateur regression: The Dutch New Herring controversies”","authors":"Jan C. Van Ours, Ben Vollaard","doi":"10.1111/sjos.12741","DOIUrl":"https://doi.org/10.1111/sjos.12741","url":null,"abstract":"","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"37 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hyperspherical kernel density estimators (KDE), which use a parametric distribution as a guide, are studied in this paper. The main benefit is that these estimators improve the bias of nonguided kernel density estimators when the parametric guiding distribution is not too far from the true density, while preserving the variance. When using a von Mises‐Fisher density as guide, the proposal performs as well as the classical KDE, even when the guiding model is incorrect, and far from the true distribution. This benefit is particular for the hyperspherical setting given its compact support, and is in contrast to similar methods for real valued data. Moreover, we deal with the important issue of data‐driven selection of the smoothing parameter. Simulations and real data examples illustrate the finite‐sample performance of the proposed method, also in comparison with other recently proposed estimation methods.
本文研究了使用参数分布作为导向的超球核密度估计器（KDE）。其主要优点是，当参数指导分布与真实密度相差不大时，这些估计器可以改善非指导核密度估计器的偏差，同时保留方差。当使用 von Mises-Fisher 密度作为指导时，即使指导模型不正确且与真实分布相差甚远，该提案的性能也不亚于经典的 KDE。考虑到超球面的紧凑支持，这种优势在超球面设置中尤为明显，这与用于实值数据的类似方法形成了鲜明对比。此外，我们还处理了数据驱动的平滑参数选择这一重要问题。模拟和真实数据实例说明了所提方法的有限样本性能，同时也与最近提出的其他估计方法进行了比较。
{"title":"Nonparametric estimation of densities on the hypersphere using a parametric guide","authors":"María Alonso‐Pena, Gerda Claeskens, Irène Gijbels","doi":"10.1111/sjos.12737","DOIUrl":"https://doi.org/10.1111/sjos.12737","url":null,"abstract":"Hyperspherical kernel density estimators (KDE), which use a parametric distribution as a guide, are studied in this paper. The main benefit is that these estimators improve the bias of nonguided kernel density estimators when the parametric guiding distribution is not too far from the true density, while preserving the variance. When using a von Mises‐Fisher density as guide, the proposal performs as well as the classical KDE, even when the guiding model is incorrect, and far from the true distribution. This benefit is particular for the hyperspherical setting given its compact support, and is in contrast to similar methods for real valued data. Moreover, we deal with the important issue of data‐driven selection of the smoothing parameter. Simulations and real data examples illustrate the finite‐sample performance of the proposed method, also in comparison with other recently proposed estimation methods.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"24 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In contrast to maximum correlation, however, our correlation coefficients allow for rank and moment‐based estimators which are simple to compute and have tractable asymptotic distributions. Confidence intervals resulting from these asymptotic approximations and the covariance bootstrap show good finite‐sample coverage. In a simulation, the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably with competing methods based on distance correlation or rank coefficients for functional dependence, among others. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners which is not shared by various competitors. We illustrate the practical usefulness of our methods in applications to two real data sets.
{"title":"Lancaster correlation: A new dependence measure linked to maximum correlation","authors":"Hajo Holzmann, Bernhard Klar","doi":"10.1111/sjos.12733","DOIUrl":"https://doi.org/10.1111/sjos.12733","url":null,"abstract":"We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In contrast to maximum correlation, however, our correlation coefficients allow for rank and moment‐based estimators which are simple to compute and have tractable asymptotic distributions. Confidence intervals resulting from these asymptotic approximations and the covariance bootstrap show good finite‐sample coverage. In a simulation, the power of asymptotic as well as permutation tests for independence based on our correlation measures compares favorably with competing methods based on distance correlation or rank coefficients for functional dependence, among others. Moreover, for the bivariate normal distribution, our correlation coefficients equal the absolute value of the Pearson correlation, an attractive feature for practitioners which is not shared by various competitors. We illustrate the practical usefulness of our methods in applications to two real data sets.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"56 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Claudio Heinrich‐Mertsching, Thordis L. Thorarinsdottir, Peter Guttorp, Max Schneider
We introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte Carlo approximations of expectations and can therefore easily be evaluated for any point process model that can be simulated. In this regard, they are more flexible than the commonly used logarithmic score and other existing proper scores for point process predictions. The scoring rules allow for evaluating the calibration of a model to specific aspects of a point process, such as its spatial distribution or tendency toward clustering. Using simulations, we analyze the sensitivity of our scoring rules to different aspects of the forecasts and compare it to the logarithmic score. Applications to earthquake occurrences in northern California, United States and the spatial distribution of Pacific silver firs in Findley Lake Reserve in Washington highlight the usefulness of our scores for scientific model selection.
{"title":"Validation of point process predictions with proper scoring rules","authors":"Claudio Heinrich‐Mertsching, Thordis L. Thorarinsdottir, Peter Guttorp, Max Schneider","doi":"10.1111/sjos.12736","DOIUrl":"https://doi.org/10.1111/sjos.12736","url":null,"abstract":"We introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte Carlo approximations of expectations and can therefore easily be evaluated for any point process model that can be simulated. In this regard, they are more flexible than the commonly used logarithmic score and other existing proper scores for point process predictions. The scoring rules allow for evaluating the calibration of a model to specific aspects of a point process, such as its spatial distribution or tendency toward clustering. Using simulations, we analyze the sensitivity of our scoring rules to different aspects of the forecasts and compare it to the logarithmic score. Applications to earthquake occurrences in northern California, United States and the spatial distribution of Pacific silver firs in Findley Lake Reserve in Washington highlight the usefulness of our scores for scientific model selection.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"57 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The multivariate coefficient of variation (MCV) is an attractive and easy‐to‐interpret effect size for the dispersion in multivariate data. Recently, the first inference methods for the MCV were proposed for general factorial designs. However, the inference methods are primarily derived for one special MCV variant while there are several reasonable proposals. Moreover, when rejecting a global null hypothesis, a more in‐depth analysis is of interest to find the significant contrasts of MCV. This paper concerns extending the nonparametric permutation procedure to the other MCV variants and a max‐type test for post hoc analysis. To improve the small sample performance of the latter, we suggest a novel bootstrap strategy and prove its asymptotic validity. The actual performance of all proposed tests is compared in an extensive simulation study and illustrated by real data analysis. All methods are implemented in the R package GFDmcv, available on CRAN.
{"title":"Inference for all variants of the multivariate coefficient of variation in factorial designs","authors":"Marc Ditzhaus, Łukasz Smaga","doi":"10.1111/sjos.12740","DOIUrl":"https://doi.org/10.1111/sjos.12740","url":null,"abstract":"The multivariate coefficient of variation (MCV) is an attractive and easy‐to‐interpret effect size for the dispersion in multivariate data. Recently, the first inference methods for the MCV were proposed for general factorial designs. However, the inference methods are primarily derived for one special MCV variant while there are several reasonable proposals. Moreover, when rejecting a global null hypothesis, a more in‐depth analysis is of interest to find the significant contrasts of MCV. This paper concerns extending the nonparametric permutation procedure to the other MCV variants and a max‐type test for post hoc analysis. To improve the small sample performance of the latter, we suggest a novel bootstrap strategy and prove its asymptotic validity. The actual performance of all proposed tests is compared in an extensive simulation study and illustrated by real data analysis. All methods are implemented in the R package GFDmcv, available on CRAN.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Professor (now emeritus) Nils Lid Hjort has through more than four decades been one of the most original and productive statisticians in Norway, contributing to a wide range of topics such as survival analysis, Bayesian nonparametrics, empirical likelihood, density estimation, focused inference, model selection, and confidence distributions. This conversation, which took place at the University of Oslo in December 2023, sheds light on how Nils Hjort's curious and open mind, coupled with a deep understanding, has enabled him to seamlessly navigate between different fields of statistics and its applications. Our aim is to encourage the statistics community to always be on the lookout for unexpected connections in statistical science and to embrace unexpected encounters with fellow statisticians from around the world.
尼尔斯-利德-希约尔特教授（现为名誉教授）四十多年来一直是挪威最具原创性和最有成就的统计学家之一，在生存分析、贝叶斯非参数、经验似然法、密度估计、重点推断、模型选择和置信度分布等广泛领域做出了贡献。这次对话于 2023 年 12 月在奥斯陆大学举行，它揭示了 Nils Hjort 如何以其好奇、开放的心态和深刻的理解力，在统计学及其应用的不同领域之间游刃有余。我们的目标是鼓励统计界始终关注统计科学中的意外联系，并与来自世界各地的统计学家同仁不期而遇。
{"title":"A conversation with Nils Lid Hjort","authors":"Ørnulf Borgan, Ingrid K. Glad","doi":"10.1111/sjos.12732","DOIUrl":"https://doi.org/10.1111/sjos.12732","url":null,"abstract":"Professor (now emeritus) Nils Lid Hjort has through more than four decades been one of the most original and productive statisticians in Norway, contributing to a wide range of topics such as survival analysis, Bayesian nonparametrics, empirical likelihood, density estimation, focused inference, model selection, and confidence distributions. This conversation, which took place at the University of Oslo in December 2023, sheds light on how Nils Hjort's curious and open mind, coupled with a deep understanding, has enabled him to seamlessly navigate between different fields of statistics and its applications. Our aim is to encourage the statistics community to always be on the lookout for unexpected connections in statistical science and to embrace unexpected encounters with fellow statisticians from around the world.","PeriodicalId":49567,"journal":{"name":"Scandinavian Journal of Statistics","volume":"6 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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