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 bΣ and of the estimated regression matrix, bΣ12 bΣ −1 22 . We obtain a representation for bΣ in terms of independent matrices, and derive its exact density function, thereby generalizing the Wishart distribution to the setting of monotone incomplete data, and obtain saddlepoint approximations for the distributions of bΣ and its partial Iwasawa coordinates. We establish the unbiasedness of a modified likelihood ratio criterion for testing H0 : Σ = Σ0, where Σ0 is a given matrix, and obtain the null and non-null distributions of the test statistic. In testing H0 : (µ, Σ) = (µ0, Σ0), where µ0 and Σ0 are given, we pro...

• Type: Journal
• Year: 2010
• Where: MA
• Authors: Wan-Ying Chang, Donald St. P. Richards
• Keywords: Communications, Incomplete Data, Likelihood Ratio Criterion, MA 2010, Non-null Distributions