Asymptotic error rates of the W and Z statistics when the training observations are dependent

摘要

In this paper consideration is given to the properties of the classification statistics W and Z, which were developed for use in discrimination problems with independent training observations. The relative behaviour of these two statistics when the training observations are dependent is investigated. For training observations following a stationary autoregressive process of order p, the asymptotic expansion of the expected error rates associated with W and Z are derived up to and including terms of the second order with respect to the reciprocals of the sample sizes. It is shown that neither Z nor W is absolutely superior to the other. Numerical results are given to show that their relative performance is dependent on the extent of correlation among the training observations and the size of the separation between the two populations, as measured by the Mahalanobis distance.