Variable Selection in Heteroscedastic Discriminant Analysis

摘要

The likelihood ratio test statistic for the identity in means and covariance matrices of k normal populations has a well-known stepdown decomposition measuring the contribution of each component of the vector observation. It is shown that this decomposition in turn gives rise to three components testing the residual homoscedasticity of each variable; the parallelism of its regression on its predecessors; and identity of location. A variety of uses of this decomposition in selecting variables is proposed.