It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on distributions.When m=1,it is done by the (traditional) hypothesis test.In this paper,a generalization to th...It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on distributions.When m=1,it is done by the (traditional) hypothesis test.In this paper,a generalization to the case m 】 1 is proposed.The fundamental difference with the case m=1 is that the new alternative hypothesis is a partition of m multiple claims and is data-dependent.Data is used to decide which claim in the partition is to be tested as the alternative.Thus,a random alternative is involved.The conditional and overall type I errors of the proposed test are controlled at a given level,and this test can be used as a new solution for the general multiple test problem.Several classical problems,including the one-sample problem,model selection in multiple linear regression,and multi-factor analysis,are revisited,and new tests are provided correspondingly.Consequently,the famous two-sided t-test should be replaced by the proposed.展开更多
This paper establishes the asymptotic independence between the quadratic form z^(T)Az and maximum max1≤i≤p|zi|of a sequence of independent sub-Gaussian random variables z=(z1m…zp)^(T).Based on this theoretical resu...This paper establishes the asymptotic independence between the quadratic form z^(T)Az and maximum max1≤i≤p|zi|of a sequence of independent sub-Gaussian random variables z=(z1m…zp)^(T).Based on this theoretical result,we find the asymptotic joint distribution for the quadratic form and maximum,which can be applied into the high-dimensional testing problems.By combining the sum-type test and the max-type test,we propose the Fisher’s combination tests for the one-sample mean test and two-sample mean test.Under this novel general framework,several strong assumptions in existing literature have been relaxed.Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.展开更多
基金supported in part by US National Science Foundation (Grant No.DMS-0906858)
文摘It is common in statistical practice that one needs to make a choice among m + 1 mutually exclusive claims on distributions.When m=1,it is done by the (traditional) hypothesis test.In this paper,a generalization to the case m 】 1 is proposed.The fundamental difference with the case m=1 is that the new alternative hypothesis is a partition of m multiple claims and is data-dependent.Data is used to decide which claim in the partition is to be tested as the alternative.Thus,a random alternative is involved.The conditional and overall type I errors of the proposed test are controlled at a given level,and this test can be used as a new solution for the general multiple test problem.Several classical problems,including the one-sample problem,model selection in multiple linear regression,and multi-factor analysis,are revisited,and new tests are provided correspondingly.Consequently,the famous two-sided t-test should be replaced by the proposed.
基金supported by the National Natural Science Foundation of China(Grant Nos.12101335 and 12271271)the Natural Science Foundation of Tianjin(Grant No.21JCQNJC00020)+4 种基金the Fundamental Research Funds for the Central Universities,Nankai University(Grant Nos.63211088 and 63221050)supported by National Natural Science Foundation of China(Grant No.12101332)supported by Shenzhen Wukong Investment Company,the Fundamental Research Funds for the Central Universities under(Grant No.ZB22000105)the China National Key R&D Program(Grant Nos.2019YFC1908502,2022YFA1003703,2022YFA1003802,2022YFA1003803)the National Natural Science Foundation of China(Grants Nos.12271271,11925106,12231011,11931001 and 11971247)。
文摘This paper establishes the asymptotic independence between the quadratic form z^(T)Az and maximum max1≤i≤p|zi|of a sequence of independent sub-Gaussian random variables z=(z1m…zp)^(T).Based on this theoretical result,we find the asymptotic joint distribution for the quadratic form and maximum,which can be applied into the high-dimensional testing problems.By combining the sum-type test and the max-type test,we propose the Fisher’s combination tests for the one-sample mean test and two-sample mean test.Under this novel general framework,several strong assumptions in existing literature have been relaxed.Monte Carlo simulation has been done which shows that our proposed tests are strongly robust to both sparse and dense data.
