Hierarchical Missing Data and Multivariate Behrens–Fisher Problem

Abstract

This article firstly defines hierarchical data missing pattern, which is a generalization of monotone data missing pattern. Then multivariate Behrens–Fisher problem with hierarchical missing data is considered to illustrate that how ideas in dealing with monotone missing data can be extended to deal with hierarchical missing pattern. A pivotal quantity similar to the Hotelling T 2 is presented, and the moment matching method is used to derive its approximate distribution which is for testing and interval estimation. The precision of the approximation is illustrated through Monte Carlo data simulation. The results indicate that the approximate method is very satisfactory even for moderately small samples.

Maximum likelihood estimation for multivariate normal distribution with hierarchical missing data

“…There are several missing patterns considered in the literature, but the incomplete data with monotone pattern not only occur frequently in practice but also it allows the exact calculation of the maximum likelihood estimators (MLEs) and the likelihood ratio statistics and relevant distributions if multivariate normality is assumed. Jianqi Yu [1] defines hierarchical data missing pattern, which is a generalization of monotone data missing pattern. Anderson [2] gave a simple approach to derive the MLEs of bivariate normal data for a special case of monotone pattern.…”