A consistent test via the partial penalized empirical likelihood approach for the parametric hy- pothesis testing under the sparse case, called the partial penalized empirical likelihood ratio （PPELR） test, is propo...A consistent test via the partial penalized empirical likelihood approach for the parametric hy- pothesis testing under the sparse case, called the partial penalized empirical likelihood ratio （PPELR） test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypoth- esis and the local alternatives of order n-1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical like- lihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11471223,11231010,11028103,11071022,11501586,71420107025)Key project of Beijing Municipal Education Commission(Grant No.KZ201410028030)the Foundation of Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘A consistent test via the partial penalized empirical likelihood approach for the parametric hy- pothesis testing under the sparse case, called the partial penalized empirical likelihood ratio （PPELR） test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypoth- esis and the local alternatives of order n-1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical like- lihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.
