{"title":"A stable sequential multiple test for Koopman–Darmois family","authors":"Shuaiyu Chen, Yan Li, Xiaolong Pu, Dongdong Xiang","doi":"10.1016/j.jspi.2023.01.006","DOIUrl":null,"url":null,"abstract":"<div><p>Assuming that data are collected sequentially from multiple streams whose density functions belong to the Koopman–Darmois family, we implement simultaneous testing on multiple hypotheses with respect to parameters. To stabilize the expected sample sizes (ESSs) at all possible values of the true parameters, we intersect individual 2-SPRT plans and propose reasonable thresholds to balance stopping rules among streams. Under two types of constrained familywise error probabilities, we prove that our method has bounded maximum expected sample sizes (MESSs) and achieves asymptotic optimality in the sense of minimizing MESSs. Simulation results demonstrate the stability of our method, in the sense of achieving smaller MESSs than those of the baseline methods. We further apply our method to a real data set.</p></div>","PeriodicalId":50039,"journal":{"name":"Journal of Statistical Planning and Inference","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Planning and Inference","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S037837582300006X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Assuming that data are collected sequentially from multiple streams whose density functions belong to the Koopman–Darmois family, we implement simultaneous testing on multiple hypotheses with respect to parameters. To stabilize the expected sample sizes (ESSs) at all possible values of the true parameters, we intersect individual 2-SPRT plans and propose reasonable thresholds to balance stopping rules among streams. Under two types of constrained familywise error probabilities, we prove that our method has bounded maximum expected sample sizes (MESSs) and achieves asymptotic optimality in the sense of minimizing MESSs. Simulation results demonstrate the stability of our method, in the sense of achieving smaller MESSs than those of the baseline methods. We further apply our method to a real data set.
期刊介绍:
The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists.
We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.