Maximum likelihood estimation of the mean of a multivariate normal population with monotone incomplete data

Given a two-step, monotone incomplete, random sample from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ, we consider the problem of deriving an exact stochastic representation for μ̂, the maximum likelihood estimator of μ. We prove that μ̂ and Σ̂, the maximum likelihood estimators of μ and Σ, respectively, are equivariant under a certain group of affine transformations, and then we apply the equivariance property to obtain a new derivation of a stochastic representation for μ̂ established by Chang and Richards (2009). The new derivation induces explicit representations, in terms of the data, for the independent random variables that arise in the stochastic representation for μ̂.