The Stein phenomenon for monotone incomplete multivariate normal data

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 b μ, the maximum likelihood estimator of μ. We obtain ellipsoidal confidence regions for μ through T , a generalization of Hotelling’s statistic. We de...

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

We continue our recent work on finite-sample, i.e., non-asymptotic, inference with two-step, monotone incomplete data from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Under the assumption that Σ is block-diagonal when partitioned according to the two-step pattern, we derive the distributions of the diagonal blocks of b Σ and of the estimated regression matrix,...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Conjugate analysis of multivariate nor- mal data with incomplete observations

The authors discuss prior distributions that are conjugate to the multivariate normal likelihood when some of the observations are incomplete. They present a general class of priors for incorporating information about unidentified parameters in the covariance matrix. They analyze the special case of monotone patterns of missing data, providing an explicit recursive form for the posterior distri...

Comparison of confidence intervals for correlation coefficients based on incomplete monotone samples and those based on listwise deletion

Inferential procedures for estimating and comparing normal correlation coefficients based on incomplete samples with a monotone missing pattern are considered. The procedures are based on the generalized variable (GV) approach. It is shown that the GVmethods based on complete or incomplete samples are exact for estimating or testing a simple correlation coefficient. Procedures based on incomple...