Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics

IF 1.2 4区 数学
M. Banerjee, J. Wellner
{"title":"Score Statistics for Current Status Data: Comparisons with Likelihood Ratio and Wald Statistics","authors":"M. Banerjee, J. Wellner","doi":"10.2202/1557-4679.1001","DOIUrl":null,"url":null,"abstract":"In this paper we introduce three natural ``score statistics\" for testing the hypothesis that F(t_0)takes on a fixed value in the context of nonparametric inference with current status data. These three new test statistics have natural interpretations in terms of certain (weighted) L_2 distances, and are also connected to natural ``one-sided\" scores. We compare these new test statistics with the analogue of the classical Wald statistic and the likelihood ratio statistic introduced in Banerjee and Wellner (2001) for the same testing problem. Under classical ``regular\" statistical problems the likelihood ratio, score, and Wald statistics all have the same chi-squared limiting distribution under the null hypothesis. In sharp contrast, in this non-regular problem all three statistics have different limiting distributions under the null hypothesis. Thus we begin by establishing the limit distribution theory of the statistics under the null hypothesis, and discuss calculation of the relevant critical points for the test statistics. Once the null distribution theory is known, the immediate question becomes that of power. We establish the limiting behavior of the three types of statistics under local alternatives. We have also compared the power of these five different statistics via a limited Monte-Carlo study. Our conclusions are: (a) the Wald statistic is less powerful than the likelihood ratio and score statistics; and (b) one of the score statistics may have more power than the likelihood ratio statistic for some alternatives.","PeriodicalId":50333,"journal":{"name":"International Journal of Biostatistics","volume":"1 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2005-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2202/1557-4679.1001","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Biostatistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2202/1557-4679.1001","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13

Abstract

In this paper we introduce three natural ``score statistics" for testing the hypothesis that F(t_0)takes on a fixed value in the context of nonparametric inference with current status data. These three new test statistics have natural interpretations in terms of certain (weighted) L_2 distances, and are also connected to natural ``one-sided" scores. We compare these new test statistics with the analogue of the classical Wald statistic and the likelihood ratio statistic introduced in Banerjee and Wellner (2001) for the same testing problem. Under classical ``regular" statistical problems the likelihood ratio, score, and Wald statistics all have the same chi-squared limiting distribution under the null hypothesis. In sharp contrast, in this non-regular problem all three statistics have different limiting distributions under the null hypothesis. Thus we begin by establishing the limit distribution theory of the statistics under the null hypothesis, and discuss calculation of the relevant critical points for the test statistics. Once the null distribution theory is known, the immediate question becomes that of power. We establish the limiting behavior of the three types of statistics under local alternatives. We have also compared the power of these five different statistics via a limited Monte-Carlo study. Our conclusions are: (a) the Wald statistic is less powerful than the likelihood ratio and score statistics; and (b) one of the score statistics may have more power than the likelihood ratio statistic for some alternatives.
当前状态数据的得分统计:与似然比和沃尔德统计的比较
在本文中,我们引入了三种自然的“分数统计”来检验F(t_0)在使用当前状态数据进行非参数推理的情况下取固定值的假设。这三个新的测试统计量在一定(加权)l2距离方面具有自然解释,并且也与自然的“片面”分数有关。我们将这些新的检验统计量与Banerjee和Wellner(2001)为同一检验问题引入的经典Wald统计量和似然比统计量的类比进行比较。在经典的“规则”统计问题中,在零假设下,似然比、分数和Wald统计量都具有相同的卡方极限分布。与此形成鲜明对比的是,在这个非正则问题中,所有三种统计量在零假设下具有不同的极限分布。因此,我们首先建立了零假设下统计量的极限分布理论,并讨论了检验统计量的相关临界点的计算。一旦知道了零分布理论,直接的问题就变成了权力的问题。建立了三种统计量在局部替代条件下的极限行为。我们还通过一项有限的蒙特卡洛研究比较了这五种不同统计数据的效力。我们的结论是:(a) Wald统计量比似然比和评分统计量更弱;(b)对于某些选项,其中一个得分统计可能比似然比统计更有效。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
International Journal of Biostatistics
International Journal of Biostatistics Mathematics-Statistics and Probability
CiteScore
2.30
自引率
8.30%
发文量
28
期刊介绍: The International Journal of Biostatistics (IJB) seeks to publish new biostatistical models and methods, new statistical theory, as well as original applications of statistical methods, for important practical problems arising from the biological, medical, public health, and agricultural sciences with an emphasis on semiparametric methods. Given many alternatives to publish exist within biostatistics, IJB offers a place to publish for research in biostatistics focusing on modern methods, often based on machine-learning and other data-adaptive methodologies, as well as providing a unique reading experience that compels the author to be explicit about the statistical inference problem addressed by the paper. IJB is intended that the journal cover the entire range of biostatistics, from theoretical advances to relevant and sensible translations of a practical problem into a statistical framework. Electronic publication also allows for data and software code to be appended, and opens the door for reproducible research allowing readers to easily replicate analyses described in a paper. Both original research and review articles will be warmly received, as will articles applying sound statistical methods to practical problems.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信