Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters
Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters
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DOI：
10.1080/01621459.1989.10478810
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发表时间：
1989-06
影响因子：
3.7
通讯作者：
Kam-Wah Tsui;Sam Weerahandi
中科院分区：
文献类型：
--
作者：
Kam-Wah Tsui;Sam Weerahandi
本文研究了单边假设H0：θ≤θ0与H1：θ>；θ0的显著性检验问题，其中θ是感兴趣的参数。在通常的设置下，设x为观测数据，T(X)为检验统计量，使得T(X)的分布族在θ中随机增加。将CX定义为{X：T(X)-T(X)≥0}。P值为p(X)=supθ≤θ0 Pr(X∈Cx|θ)。在存在干扰参数η的情况下，可能不存在具有独立于η的p值的非平凡Cx。我们考虑基于形式为Cx(θ，η)={X：T(x；x，θ，η)≥T(x；x，θ，η)}的广义极值区域的检验，并给出了关于T(X；x，θ，η)的条件，使得p值p(X)=supθ≤θ0 Pr(X∈Cx(θ，η))不含扰动参数η，其中T在θ中随机递增。我们给出了一个关于两个独立指数分布均值差异的假设检验问题的解决方案，对于这个问题，固定水平检验方法是...
Abstract This article examines some problems of significance testing for one-sided hypotheses of the form H 0 : θ ≤ θ 0 versus H 1 : θ > θ 0, where θ is the parameter of interest. In the usual setting, let x be the observed data and let T(X) be a test statistic such that the family of distributions of T(X) is stochastically increasing in θ. Define Cx as {X : T(X) — T(x) ≥ 0}. The p value is p(x) = sup θ≤θ0 Pr(X ∈ Cx | θ). In the presence of a nuisance parameter η, there may not exist a nontrivial Cx with a p value independent of η. We consider tests based on generalized extreme regions of the form Cx (θ, η) = {X : T(X; x, θ, η) ≥ T(x; x, θ, η)}, and conditions on T(X; x, θ, η) are given such that the p value p(x) = sup θ≤θ0 Pr(X ∈ Cx (θ, η)) is free of the nuisance parameter η, where T is stochastically increasing in θ. We provide a solution to the problem of testing hypotheses about the differences in means of two independent exponential distributions, a problem for which the fixed-level testing approach...