Asymptotic Properties of Weighted M-estimators for variable probability samples
Econometrica · 1999 · Volume 67 · Issue 6
Abstract
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.
Keywords
Stratified sampling, variable probability sampling, multinomial sampling, exogenous sampling, weighted M-estimator, weighted least squares.
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