Conditional Tests with an Order Restriction as a Null Hypothesis
Conditional Tests with an Order Restriction as a Null Hypothesis
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DOI：
10.1007/978-1-4613-9940-7_15
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发表时间：
1986
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影响因子：
--
通讯作者：
P. Wollan;R. Dykstra
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文献类型：
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作者：
P. Wollan;R. Dykstra
对于保序正态均值问题，Bartholomew（1961）讨论了HO的条件似然比检验：均值是齐次的，而H1：均值满足线性序。他的结论是，条件检验的效力远低于卡方检验。测试H1VS。H2：所有备选方案，相应的条件检验可能比卡方检验更强大。这些条件检验在渐近正态分布参数的同时不等式约束的一般检验中特别有意义，其中对应于p（Q.，K）的很难获得。在此一般情况下，似然比统计量是asymp totically卡巴平方时，真正的参数向量位于H1，我们概述了一个新的证明Silvey定理的基础上，一个约束估计及其相应的向量的拉格朗日乘子是渐近正常的和独立的。
For the isotonic normal means problem, Bartholomew (1961) discussed a conditional likelihood-ratio test of HO: the means are homogeneous, vs. H1: the means satisfy the linear order. He concluded that the conditional test was substantially less powerful than the chi-bar-squared test. However, for testing H1vs. H2: all alternatives, the corresponding conditional test can be more powerful than the chi-bar-square test. Moreover, the conditional test can be modified so as to be asymptotically α-similar.These conditional tests are of particular interest in general tests of simultaneous inequality constraints on parameters of asymptotically normal distributions, for which the coefficients corresponding to the p(Q.,k)’s are difficult to obtain. In this general context, the likelihood ratio statistic is asymp totically chi-bar-squared whenever the true parameter vector lies in H1; we outline a new proof based on Silvey’s theorem that a constrained estimate and its corresponding vector of Lagrange multipliers are asymptotically normal and independent.