Recently R. S. Singh has studied the empirical Bayes (EB) estimation in a multiple linearregression model. In this paper we consider the EB test of regression coefficient β for this model. Wework out the EB test deci...Recently R. S. Singh has studied the empirical Bayes (EB) estimation in a multiple linearregression model. In this paper we consider the EB test of regression coefficient β for this model. Wework out the EB test decision rule by using kernel estimation of multivariate density function and itsfirst order partial derivatives. We obtain its asymptotically optimal (a. o.) property under thecondition E||β||_1<∞. It is shown that tbe convergence rates of this EB test decision rule areO(n^(-(r-1)λ/p+r)) under the condition E||β||^(pr/2-λ)<∞. where an integer r> 0<X<1 and p is the dimensionof the vector.展开更多
In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased est...In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.展开更多
基金project is supported by National Natural Science Foundation of China
文摘Recently R. S. Singh has studied the empirical Bayes (EB) estimation in a multiple linearregression model. In this paper we consider the EB test of regression coefficient β for this model. Wework out the EB test decision rule by using kernel estimation of multivariate density function and itsfirst order partial derivatives. We obtain its asymptotically optimal (a. o.) property under thecondition E||β||_1<∞. It is shown that tbe convergence rates of this EB test decision rule areO(n^(-(r-1)λ/p+r)) under the condition E||β||^(pr/2-λ)<∞. where an integer r> 0<X<1 and p is the dimensionof the vector.
基金supported by National Natural Science Foundation of China(Grant Nos.11201452 and 11271346)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402120017)the Fundamental Research Funds for the Central Universities(Grant No.WK0010000052)
文摘In this paper, the Bayes estimator and the parametric empirical Bayes estimator(PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator(MVUE) and a revised James-Stein estimators(RJSE) are investigated respectively under mean square error(MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion.
