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...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.展开更多
剂量反应的趋势测试是在药的一个中央问题。这份报纸对待比较伞模式处理效果的问题。在订的 m = g ( x ni )下面+ ni ni ( 1 i n ) ni 2 = f ( u ni )，设计点( x ni ， u ni )被知道并且非随机， g (獥杩獮挠湯楳敤敲?湩琠楨?...剂量反应的趋势测试是在药的一个中央问题。这份报纸对待比较伞模式处理效果的问题。在订的 m = g ( x ni )下面+ ni ni ( 1 i n ) ni 2 = f ( u ni )，设计点( x ni ， u ni )被知道并且非随机， g (獥杩獮挠湯楳敤敲?湩琠楨?慰数?污潳栠癡?桴?慭楸畭?畮扭牥漠?潣灭畯摮?牡慲杮摥椠?展开更多
Hypothesis test on the population mean with various inequality constraints is studied in this paper.The empirical likelihood method is applied to construct test statistics.Limiting distributions of the empirical likel...Hypothesis test on the population mean with various inequality constraints is studied in this paper.The empirical likelihood method is applied to construct test statistics.Limiting distributions of the empirical likelihood ratio test statistics are proven to be a weighted mixture of chi-square distributions.Numerical results are presented to show the validity of the proposed method.展开更多
基金Supported by the National Natural Science Foundation of China(No.71161011)
文摘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.
基金supported by the National Natural Science Foundation of China under Grant No.10771163
文摘剂量反应的趋势测试是在药的一个中央问题。这份报纸对待比较伞模式处理效果的问题。在订的 m = g ( x ni )下面+ ni ni ( 1 i n ) ni 2 = f ( u ni )，设计点( x ni ， u ni )被知道并且非随机， g (獥杩獮挠湯楳敤敲?湩琠楨?慰数?污潳栠癡?桴?慭楸畭?畮扭牥漠?潣灭畯摮?牡慲杮摥椠?
基金supported by National Nature Science Foundation of China(Grant No.10731010),National Nature Science Fund for Creative Research Groups(GrantNo.10721101)Key Fund of Yunnan Province(Grant No.2010CC003)
文摘Hypothesis test on the population mean with various inequality constraints is studied in this paper.The empirical likelihood method is applied to construct test statistics.Limiting distributions of the empirical likelihood ratio test statistics are proven to be a weighted mixture of chi-square distributions.Numerical results are presented to show the validity of the proposed method.
