Pub Date : 2025-04-03DOI: 10.1080/00031305.2025.2486306
Min Ju Lee, Na Young Yoo, Ji Hwan Cha
In this paper, we develop a new general class of discrete bivariate distributions that can model the effect of the so-called ‘load-sharing configuration’. Under such load-sharing configuration, after the failure of one component, the surviving component has to shoulder extra load, which eventually results in its failure at an earlier time than what is expected under the case of independence. To model such effect, in this paper, the residual lifetime of the surviving component is assumed to be shortened according to the usual stochastic order. We derive the joint probability mass function, the joint survival function and the marginal distributions. The identifiability of the proposed model is thoroughly investigated. We discuss a bivariate ageing property of the developed class. It will be seen that the obtained joint distribution can be expressed in terms of existing underlying distributions, which increases the applicability of the developed bivariate distributions. It will also be shown that the developed class has a high degree of flexibility in the sense that numerous families of distributions can be generated just by specifying different underlying distributions and different parameter functions for modeling stochastic dependence. Some specific families of discrete bivariate distributions which can be usefully applied in practice are obtained, and their usefulness is illustrated by some real data set analyses.
{"title":"A New General Class of Discrete Bivariate Distributions Constructed by the Usual Stochastic Order","authors":"Min Ju Lee, Na Young Yoo, Ji Hwan Cha","doi":"10.1080/00031305.2025.2486306","DOIUrl":"https://doi.org/10.1080/00031305.2025.2486306","url":null,"abstract":"In this paper, we develop a new general class of discrete bivariate distributions that can model the effect of the so-called ‘load-sharing configuration’. Under such load-sharing configuration, after the failure of one component, the surviving component has to shoulder extra load, which eventually results in its failure at an earlier time than what is expected under the case of independence. To model such effect, in this paper, the residual lifetime of the surviving component is assumed to be shortened according to the usual stochastic order. We derive the joint probability mass function, the joint survival function and the marginal distributions. The identifiability of the proposed model is thoroughly investigated. We discuss a bivariate ageing property of the developed class. It will be seen that the obtained joint distribution can be expressed in terms of existing underlying distributions, which increases the applicability of the developed bivariate distributions. It will also be shown that the developed class has a high degree of flexibility in the sense that numerous families of distributions can be generated just by specifying different underlying distributions and different parameter functions for modeling stochastic dependence. Some specific families of discrete bivariate distributions which can be usefully applied in practice are obtained, and their usefulness is illustrated by some real data set analyses.","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"44 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143933217","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}
Pub Date : 2025-04-03DOI: 10.1080/00031305.2024.2432884
M.-A. C. Bind, D. B. Rubin
Consider a study whose primary results are “not statistically significant”. How often does it lead to the following published conclusion that “there is no effect of the treatment/exposure on the outcome”? We believe too often and that the requirement to report counternull values could help to avoid this! In statistical parlance, the null value of an estimand is a value that is distinguished in some way from other possible values, for example a value that indicates no difference between the general health status of those treated with a new drug versus a traditional drug. A counternull value is a nonnull value of that estimand that is supported by the same amount of evidence that supports the null value. Of course, such a definition depends critically on how “evidence” is defined. Here, we consider the context of a randomized experiment where evidence is summarized by the randomization-based p-value associated with a specified sharp null hypothesis. Consequently, a counternull value has the same p-value from the randomization test as does the null value; the counternull value is rarely unique, but rather comprises a set of values. We explore advantages to reporting a counternull set in addition to the p-value associated with a null value; a first advantage is pedagogical, in that reporting it avoids the mistake of implicitly accepting a not-rejected null hypothesis; a second advantage is that the effort to construct a counternull set can be scientifically helpful by encouraging thought about nonnull values of estimands. Two examples are used to illustrate these ideas.
{"title":"Counternull Sets in Randomized Experiments","authors":"M.-A. C. Bind, D. B. Rubin","doi":"10.1080/00031305.2024.2432884","DOIUrl":"https://doi.org/10.1080/00031305.2024.2432884","url":null,"abstract":"Consider a study whose primary results are “not statistically significant”. How often does it lead to the following published conclusion that “there is no effect of the treatment/exposure on the outcome”? We believe too often and that the requirement to report counternull values could help to avoid this! In statistical parlance, the null value of an estimand is a value that is distinguished in some way from other possible values, for example a value that indicates no difference between the general health status of those treated with a new drug versus a traditional drug. A counternull value is a nonnull value of that estimand that is supported by the same amount of evidence that supports the null value. Of course, such a definition depends critically on how “evidence” is defined. Here, we consider the context of a randomized experiment where evidence is summarized by the randomization-based <i>p</i>-value associated with a specified sharp null hypothesis. Consequently, a counternull value has the same <i>p</i>-value from the randomization test as does the null value; the counternull value is rarely unique, but rather comprises a <i>set</i> of values. We explore advantages to reporting a counternull set in addition to the <i>p</i>-value associated with a null value; a first advantage is pedagogical, in that reporting it avoids the mistake of implicitly accepting a not-rejected null hypothesis; a second advantage is that the effort to construct a counternull set can be scientifically helpful by encouraging thought about nonnull values of estimands. Two examples are used to illustrate these ideas.","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143933219","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}
Pub Date : 2025-04-03DOI: 10.1080/00031305.2025.2459438
John M. Hoenig
This book is available in hardcover and as downloadable chapters on the internet. The author states he wants “to provide you with the tools to both select and create graphs that present data as cle...
{"title":"Modern Data Visualization with R","authors":"John M. Hoenig","doi":"10.1080/00031305.2025.2459438","DOIUrl":"https://doi.org/10.1080/00031305.2025.2459438","url":null,"abstract":"This book is available in hardcover and as downloadable chapters on the internet. The author states he wants “to provide you with the tools to both select and create graphs that present data as cle...","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"51 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143933232","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}
Pub Date : 2025-04-03DOI: 10.1080/00031305.2024.2422933
Daniel R. Jeske
A control group versus treatment group design is considered where the responses in the treatment group are modeled as a two-component mixture model that accounts for the possibility that only a fraction of the patients in the treated group will respond to the treatment. In this setting, the treatment effect is generalized to include both the fraction of treated patients that respond to the treatment and the magnitude of the response. Two alternative correlated and biased estimators are combined to yield an estimator that is preferable to either one of the estimators individually. The combined estimator is demonstrated on an illustrative blood pressure dataset.
{"title":"Estimation of a Generalized Treatment Effect in a Control Group Versus Treatment Group Design","authors":"Daniel R. Jeske","doi":"10.1080/00031305.2024.2422933","DOIUrl":"https://doi.org/10.1080/00031305.2024.2422933","url":null,"abstract":"A control group versus treatment group design is considered where the responses in the treatment group are modeled as a two-component mixture model that accounts for the possibility that only a fraction of the patients in the treated group will respond to the treatment. In this setting, the treatment effect is generalized to include both the fraction of treated patients that respond to the treatment and the magnitude of the response. Two alternative correlated and biased estimators are combined to yield an estimator that is preferable to either one of the estimators individually. The combined estimator is demonstrated on an illustrative blood pressure dataset.","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"118 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143933337","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}
Pub Date : 2024-11-05DOI: 10.1080/00031305.2024.2423814
Giovanni Nattino, Robert Ashmead, Bo Lu
Probability surveys are a major source of population representative data for policy research and program evaluation. However, the data come with the added complications of being observational and s...
{"title":"Causal Inference with Complex Surveys: A Unified Perspective on Sample Selection and Exposure Selection","authors":"Giovanni Nattino, Robert Ashmead, Bo Lu","doi":"10.1080/00031305.2024.2423814","DOIUrl":"https://doi.org/10.1080/00031305.2024.2423814","url":null,"abstract":"Probability surveys are a major source of population representative data for policy research and program evaluation. However, the data come with the added complications of being observational and s...","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"42 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142588644","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}
Pub Date : 2024-10-29DOI: 10.1080/00031305.2024.2421370
Tingxuan Wu, Cindy Feng, Longhai Li
Accurate model performance assessment in survival analysis is imperative for robust predictions and informed decision-making. Traditional residual diagnostic tools like martingale and deviance resi...
{"title":"Cross-validatory Z-Residual for Diagnosing Shared Frailty Models","authors":"Tingxuan Wu, Cindy Feng, Longhai Li","doi":"10.1080/00031305.2024.2421370","DOIUrl":"https://doi.org/10.1080/00031305.2024.2421370","url":null,"abstract":"Accurate model performance assessment in survival analysis is imperative for robust predictions and informed decision-making. Traditional residual diagnostic tools like martingale and deviance resi...","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"45 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142588642","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}
Pub Date : 2024-10-29DOI: 10.1080/00031305.2024.2421361
Sergio Díaz-Aranda, Jose Aguilar, Juan Marcos Ramírez, David Rabanedo, Antonio Fernández Anta, Rosa E. Lillo
The Network Scale-up Methods (NSUM) are methods to estimate unknown populations based on indirect surveys in which the participants provide information about aggregated data of their acquaintances....
{"title":"Performance Analysis of NSUM Estimators in Social-Network Topologies","authors":"Sergio Díaz-Aranda, Jose Aguilar, Juan Marcos Ramírez, David Rabanedo, Antonio Fernández Anta, Rosa E. Lillo","doi":"10.1080/00031305.2024.2421361","DOIUrl":"https://doi.org/10.1080/00031305.2024.2421361","url":null,"abstract":"The Network Scale-up Methods (NSUM) are methods to estimate unknown populations based on indirect surveys in which the participants provide information about aggregated data of their acquaintances....","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"8 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142588641","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}
Pub Date : 2024-10-15DOI: 10.1080/00031305.2024.2413081
Bernhard Klar
We propose a mean functional that exists for arbitrary probability distributions and characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in shar...
{"title":"A Pareto tail plot without moment restrictions","authors":"Bernhard Klar","doi":"10.1080/00031305.2024.2413081","DOIUrl":"https://doi.org/10.1080/00031305.2024.2413081","url":null,"abstract":"We propose a mean functional that exists for arbitrary probability distributions and characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in shar...","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142490347","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}
Pub Date : 2024-10-07DOI: 10.1080/00031305.2024.2408007
Fabian Obster, Christian Heumann
For grouped covariates, we propose a framework for boosting that allows for sparsity within and between groups. By using component-wise and group-wise gradient ridge boosting simultaneously with ad...
{"title":"Sparse-group boosting: Unbiased group and variable selection","authors":"Fabian Obster, Christian Heumann","doi":"10.1080/00031305.2024.2408007","DOIUrl":"https://doi.org/10.1080/00031305.2024.2408007","url":null,"abstract":"For grouped covariates, we propose a framework for boosting that allows for sparsity within and between groups. By using component-wise and group-wise gradient ridge boosting simultaneously with ad...","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"6 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142384284","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}
Pub Date : 2024-09-25DOI: 10.1080/00031305.2024.2407495
Peiyao Huang, Shuwei Li, Xinyuan Song
With the rapid development of data acquisition and storage space, massive data sets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To a...
{"title":"Additive Hazards Regression Analysis of Massive Interval-Censored Data via Data Splitting","authors":"Peiyao Huang, Shuwei Li, Xinyuan Song","doi":"10.1080/00031305.2024.2407495","DOIUrl":"https://doi.org/10.1080/00031305.2024.2407495","url":null,"abstract":"With the rapid development of data acquisition and storage space, massive data sets exhibited with large sample size emerge increasingly and make more advanced statistical tools urgently need. To a...","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":"29 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142321120","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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