Shrinkage Estimation with General Loss Functions: An Application of Stochastic Dominace Theory
用随机占优理论分析了一类广泛损失函数下的收缩估计，推荐了高斯无偏估计的收缩因子区间，并证明无偏估计被有偏估计占优，对宏观经济模型中的预期形成有启示。
Shrinkage estimation is analyzed using stochastic dominance theory over a broad class of loss functions. (Neither symmetry nor boundedness is imposed.) A recommended shrinkage factor interval is calculated for gaussian, unbiased estimators based on this analysis. Since the minimum MSE estimator is generally found to lie within this interval for t 2 1, these results justify the minimum MSE criterion as a desideratum over a wide class of loss functions. Also, the unbiased estimator is found to be dominated by shrunken (biased) estimators over a number of loss function classes. This implies that the unbiased linear projections used to model expectations formation in neoclassical macroeconomic models are stochastically dominated by biased expectations. Finally, practical shrinkage factors are given which are shown to provide modest improvements in expected losses over a wide range of symmetric and asymmetric loss functions.