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Asymptotic Properties of Weighted M‐estimators for variable probability samples
Author(s) -
Wooldridge Jeffrey M.
Publication year - 1999
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00083
Subject(s) - mathematics , estimator , weighting , statistics , multinomial distribution , variable (mathematics) , mathematical analysis , medicine , radiology
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.