Symmetry, Regression Design, and Sampling Distributions
对称性、回归设计与抽样分布
When values of regressors are symmetrically disposed, many M -estimators in a wide class of models have a reflection property, namely, that as the signs of the coefficients on regressors are reversed, their estimators' sampling distribution is reflected about the origin. When the coefficients are zero, sign reversal can have no effect. So in this case, the sampling distribution of regression coefficient estimators is symmetric about zero, the estimators are median unbiased…