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Acta Mathematicae Applicatae Sinica, English Series 2013, Vol. 29 Issue (4) :809-822    DOI: 10.1007/s10255-013-0257-8
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Comparison of Two Variances Under Inequality Constraints by Using Empirical Likelihood Method
Guo-hua DENG
School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China
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Abstract In this article, the empirical likelihood introduced by Owen Biometrika, 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.
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Guo-hua DENG
Keywordschi-bar square   empirical likelihood   inequality constraint   least favorable set     
Abstract: In this article, the empirical likelihood introduced by Owen Biometrika, 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.
Keywordschi-bar square,   empirical likelihood,   inequality constraint,   least favorable set     
Received: 2012-11-07;
Fund:

Supported by the National Natural Science Foundation of China (No. 71161011).

Cite this article:   
Guo-hua DENG .Comparison of Two Variances Under Inequality Constraints by Using Empirical Likelihood Method[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2013,V29(4): 809-822
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-013-0257-8      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2013/V29/I4/809
 
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