Upcoming Conferences

Abstract: We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from a multivariate normal population. We derive stochastic representations for the distributions of the maximum likelihood estimators of the population mean vector and covariance matrix.  By means of these stochastic representations, we provide a panoply of results pertaining to inference on the population mean vector, including ellipsoidal confidence regions for the mean vector, confidence regions for linear combinations of the components of that vector, ellipsoidal prediction regions for future complete observations from the population, and unbiasedness results for a variety of testing problems on the mean vector and covariance matrix.  For the problem of shrinkage estimation in this context, we show that analogs of the James-Stein estimator return lower risk than the maximum likelihood estimator of the population mean vector.