论文检索

广义残差方差的最优完全等变估计量的不可容许性AI 解读

The estimation of the generalized residual variance is considered when an observable Wishart random matrix is available. It is shown that when the loss function is normalized squared error, the natural fully equivariant estimator is dominated by an alternative. The latter uses either one of two estimators depending on the result of a preliminary test of significance. This alternate estimator has an everywhere smaller mean normalized squared error than the natural estimator.

利用分区多项式推导多元正态均值与回归系数估计的无偏风险估计量AI 解读

Unbiased risk estimators are derived for estimators in certain classes of equivariant estimators of multinormal matrix means, $\xi,$ and regression coefficients $\beta.$ In all cases the covariance matrix is unknown. The underlying method, a multivariate version of that of James and Stein (1960), uses zonal polynomial expansions for the distributions of noncentral statistics. This gives, in one case, the required generalization of the Pitman-Robbins representation of…