{"title":"p值的非均匀性可以在发散维数的早期出现。","authors":"Yingying Fan, Emre Demirkaya, Jinchi Lv","doi":"","DOIUrl":null,"url":null,"abstract":"<p><p>Evaluating the joint significance of covariates is of fundamental importance in a wide range of applications. To this end, p-values are frequently employed and produced by algorithms that are powered by classical large-sample asymptotic theory. It is well known that the conventional p-values in Gaussian linear model are valid even when the dimensionality is a non-vanishing fraction of the sample size, but can break down when the design matrix becomes singular in higher dimensions or when the error distribution deviates from Gaussianity. A natural question is when the conventional p-values in generalized linear models become invalid in diverging dimensions. We establish that such a breakdown can occur early in nonlinear models. Our theoretical characterizations are confirmed by simulation studies.</p>","PeriodicalId":50161,"journal":{"name":"Journal of Machine Learning Research","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7079742/pdf/","citationCount":"0","resultStr":"{\"title\":\"Nonuniformity of P-values Can Occur Early in Diverging Dimensions.\",\"authors\":\"Yingying Fan, Emre Demirkaya, Jinchi Lv\",\"doi\":\"\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>Evaluating the joint significance of covariates is of fundamental importance in a wide range of applications. To this end, p-values are frequently employed and produced by algorithms that are powered by classical large-sample asymptotic theory. It is well known that the conventional p-values in Gaussian linear model are valid even when the dimensionality is a non-vanishing fraction of the sample size, but can break down when the design matrix becomes singular in higher dimensions or when the error distribution deviates from Gaussianity. A natural question is when the conventional p-values in generalized linear models become invalid in diverging dimensions. We establish that such a breakdown can occur early in nonlinear models. Our theoretical characterizations are confirmed by simulation studies.</p>\",\"PeriodicalId\":50161,\"journal\":{\"name\":\"Journal of Machine Learning Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7079742/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Machine Learning Research\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Machine Learning Research","FirstCategoryId":"94","ListUrlMain":"","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Nonuniformity of P-values Can Occur Early in Diverging Dimensions.
Evaluating the joint significance of covariates is of fundamental importance in a wide range of applications. To this end, p-values are frequently employed and produced by algorithms that are powered by classical large-sample asymptotic theory. It is well known that the conventional p-values in Gaussian linear model are valid even when the dimensionality is a non-vanishing fraction of the sample size, but can break down when the design matrix becomes singular in higher dimensions or when the error distribution deviates from Gaussianity. A natural question is when the conventional p-values in generalized linear models become invalid in diverging dimensions. We establish that such a breakdown can occur early in nonlinear models. Our theoretical characterizations are confirmed by simulation studies.
期刊介绍:
The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online.
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JMLR seeks previously unpublished papers on machine learning that contain:
new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature;
experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems;
accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods;
formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks;
development of new analytical frameworks that advance theoretical studies of practical learning methods;
computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.