A Preliminary Test for Discriminant Analysis Based on Small Samples.

摘要

Consider two populations having p-variate normal distributions with a common variance-covariance matrix where the parameters are to be estimated from small samples. Letting X denote the vector of observations on an experimental unit, whose origin is uncertain, a test is proposed for the null hypothesis against the alternative that X is distributed according to a third unspecified distribution. It is shown that the critical region can be selected so that its size is known to be between alpha and alpha/2, inclusive, for any desired value of alpha. The test is illustrated by an application to a taxonomy problem.