Asymptotic Properties of Weighted M-estimators for variable probability samples
系统分析了变概率分层抽样下加权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，并比较了加权与未加权估计量的效率。
I provide a systematic treatment of the asymptotic properties of weighted M-estimators under variable probability stratified sampling. The characterization of the sampling scheme and representation of the objective function allow for a straightforward analysis. Simple, consistent asymptotic variance matrix estimators are proposed for a large class of problems. When stratification is based on exogenous variables, I show that the unweighted M-estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality. When population frequencies are known, a more efficient weighting is possible. I also show how the results carry over to multinomial sampling.