Some basic properties of the maximum likelihood estimators for a multivariate normal distribution with monotone missing data

In this paper we study some basic properties of the MLEs &mucirc; and &Sigmacrc; 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 &mucirc; and the exact bias of &Sigmacrc;. 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 MLEs of μ and the usual transformed matrix Δ of Σ are given in explicit forms. Some analogous properties are also obtained.