Improved estimates for moments by observations from mixtures

Abstract

Abstract. Procedures for improving weighted empirical distribution functions constructed from mixtures with varying concentrations are considered. The procedures are such that the estimators of moments of the mixture components constructed from weighted empirical distribution functions have specified properties (say, estimators of the variance must not be negative). We prove that the moment estimators constructed from improved weighted empirical distribution functions have the same asymptotic behavior as those constructed from the original weighted empirical distribution functions.