Bayesian Estimation and Prediction Using Asymmetric Loss Functions
针对Varian的非对称LINEX损失函数，推导了多种经典模型的最优估计量和预测量，并证明某些常用估计量（如样本均值、最小二乘回归系数）在该损失下不可容许，存在风险更优的替代估计量。
Abstract Estimators and predictors that are optimal relative to Varian's asymmetric LINEX loss function are derived for a number of well-known models. Their risk functions and Bayes risks are derived and compared with those of usual estimators and predictors. It is shown that some usual estimators, for example, a scalar sample mean or a scalar least squares regression coefficient estimator, are inadmissible relative to asymmetric LINEX loss by providing alternative estimators that dominate them uniformly in terms of risk. Key Words: Asymmetric loss functionInadmissibilityEstimationPredictionRisk functionRobustness