Stabilized multivariate tests : the inclusion of missing values

In two recent papers, LAUTER (1996) and LAUTER, GLIMM, and KROPF (1996) have proposed a new class of exact tests for multivariate normal data with an inherent structure. These tests are based on the construction of scores that have a spherical distribution. The principle can be adapted to a variety of different situations, and it supports exact tests with small samples of high-dimensional data. In this paper, an enhancement of that theory will be given regarding the problem of missing data. It provides a new mathematical understanding of mean imputation techniques, and it is also the basis for a modified principal component missing data algorithm described here.