Chapter 3 - Inference on Parameters of Multivariate Normal Populations When Some Data is Missing

Abstract

Much of the literature on multivariate analysis is devoted to problems of inference when the same set of measurements is taken on each observed individual event. But in practice, such a situation is not always realized, because of the inherent nature of the population sampled, as with skeletal material, in which not all observations can be taken on each specimen or the nature of the phase sampling employed. To derive a test in a given problem, one of the following procedures is used: (1) the ad hoc or intuitive approach; (2) the likelihood ratio (LR) principle; (3) an approach via the completeness of an exponential family to obtain a uniformly most powerful unbiased (UM PU) test or simple similar or unbiased tests; and (4) an invariance principle, which helps to get an UMPI or locally best invariant (LBI) test.