Comparison of two variances under inequality constraints by using empirical likelihood method
Comparison of two variances under inequality constraints by using empirical likelihood method
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DOI：
10.1007/s10255-013-0257-8
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发表时间：
2013-10
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通讯作者：
Guo-hua Deng
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作者：
Guo-hua Deng
本文应用OwenBiometrika，75，237-249（1988）提出的经验似然检验方法，检验了参数空间上两个总体在不等式约束下的方差。我们做这个研究的一个原因是因为这方面的许多文献仅限于检验一个总体或多个总体的均值;另一个但更重要的原因是：即使考虑两个或多个总体，参数空间也总是没有约束的。实际上，具有某种约束的参数空间可以在任何地方满足。在这种情况下，营养参数是不可避免的，使估计不稳定。因此，对它的分析变得相当复杂。我们的工作主要集中在不等式约束下相对复杂的两个方差的检验问题上，而两个均值的检验问题则是其简单的推理问题。我们证明了经验似然比检验统计量的极限分布是单个卡方分布或两个等权卡方分布的混合分布。
In this article, the empirical likelihood introduced by OwenBiometrika, 75, 237–249 (1988) is applied to test the variances of two populations under inequality constraints on the parameter space. One reason that we do the research is because many literatures in this area are limited to testing the mean of one population or means of more than one populations; the other but much more important reason is: even if two or more populations are considered, the parameter space is always without constraint. In reality, parameter space with some kind of constraints can be met everywhere. Nuisance parameter is unavoidable in this case and makes the estimators unstable. Therefore the analysis on it becomes rather complicated. We focus our work on the relatively complicated testing issue over two variances under inequality constraints, leaving the issue over two means to be its simple ratiocination. We prove that the limiting distribution of the empirical likelihood ratio test statistic is either a single chi-square distribution or the mixture of two equally weighted chi-square distributions.