Some Basic Properties of the Mle's for a Multivariate Normal Distribution with Monotone Missing Data

Abstract

SYNOPTIC ABSTRACTIn this paper we study some basic properties of the MLE's and for a p-variate normal population Np(μ, Σ), based on a k-step monotone sample. For k = 2 and 3, we obtain the exact means and variances of and the exact bias of . Asymptotic expansions of the distributions of these estimators are also obtained in the situation when the sample size is large. For a general k, the MLE's of μ and the usual transformed matrix Δ of Σ are given in explicit forms. Some analogous properties are also obtained.