Discrimination, Allocatory and Separatory, Linear Aspects

Publisher Summary This chapter discusses the twin goals of linear discrimination, that is, allocation and separation. It reviews linearity in the mutivariate normal case and discusses the extent to which linearity is optimal. The exact linear theory is strictly appropriate for restricted sets of distributional assumptions, though the linear theory is somewhat wider than the logistic family. However, the linear theory gives reasonably robust, if less than optimal, solutions to many cases. However, there are situations where the linear theory should not be applied, for example, where two normal populations have the same mean but differ in their covariance matrices. In this situation, the linear discriminants will be quite inappropriate. However, the logistic model encompasses a variety of possible distributional assumptions. While presumably robust for its class when its parameters are estimated, it is not expected to yield as efficient a procedure when compared to one based on the true member of the class.

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