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
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.
