Abstract
One common objective of many multivariate techniques is to achieve a reduction in dimensionality while at the same time retain most of the relevant information contained in the original data set. This reduction not only provides a parsimonious description of the data but, in many cases, also increases the reliability of subsequent analyses of the data. In this paper we consider the problem of determining the minimum dimension necessary for quadratic discrimination in normal populations with heterogeneous covariance matrices. Some asymptotic chi-squared tests are obtained. Simulations are used to investigate the adequacy of the chi-squared approximations and to compare the misclassification probabilities of reduced-dimension quadratic discrimination with full-dimension quadratic discrimination.
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