ASYMPTOTIC PROPERTIES OF WEIGHTED M-ESTIMATORS FOR STANDARD STRATIFIED SAMPLES
系统研究了标准分层抽样下加权M估计量的渐近性质，提出了简单一致的渐近方差矩阵估计量，并推导了用于检验抽样方案外生性的Hausman检验。
I provide a systematic treatment of the asymptotic properties of weighted M -estimators under standard stratified sampling. Simple, consistent asymptotic variance matrix estimators are proposed for a broad class of problems. When stratification is based on exogenous variables, I show that the usual, unweighted M -estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality. Hausman tests for the exogeneity of the sampling scheme, including fully robust forms, are derived.