Finite-sample inference with monotone incomplete multivariate normal data, I

We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. We derive a stochastic representation for the exact distribution of μ̂, the maximum likelihood estimator of μ. We obtain ellipsoidal confidence regions for μ through T2T2, a generalization of Hotelling’s statistic. We derive the asymptotic distribution of, and probability inequalities for, T2T2 under various assumptions on the sizes of the complete and incomplete samples. Further, we establish an upper bound for the supremum distance between the probability density functions of μ̂ and μ˜, a normal approximation to μ̂.