Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean
异方差正态均值的分组线性经验贝叶斯估计
The problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical Bayes estimators. By taking a different approach that treats the known variances as part of the random observations, we restore symmetry and thus the effectiveness of such methods. We suggest a group-linear empirical Bayes estimator, which collects observations with similar variances and applies a…