Econometrica: Nov 1999, Volume 67, Issue 6
Asymptotic Properties of Weighted M‐estimators for variable probability samples
Jeffrey M. WooldridgeI 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.
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