An Estimation Procedure for Mixtures of Distributions

Abstract

The symbols for estimators in this paper have been printed in light italic type. This is an exception from our usual typographic convention of showing matrices and vector quantities in bold black type, since in this case the large number of such symbols would seriously interfere with readability. A general method is proposed for estimating the mixing measures of combinations of known distributions. The method is applicable to continuous and discrete mixtures. The small sample behaviour of the method is investigated by Monte Carlo methods. In large samples it is shown that the estimator converges to the true mixing measure with probability 1 at the rate of almostO(n-½) and has an asymptotic normal distribution.