Department of Statistics Seminar
North Carolina State University

presents

Donald Richards

University of Virginia

"Exact Misclassification Probabilities for Plug-In Normal Quadratic Discriminant Functions"

ABSTRACT

We consider the problem of discriminating, on the basis of random ``training'' samples, between two independent multivariate normal populations which have a common mean vector and distinct covariance matrices. We apply the theory of Bessel functions of matrix argument to derive stochastic representations for the exact distributions of the ``plug-in'' quadratic discriminant functions. These stochastic representations involve only chi-squared and F- distributions, and are an efficient method for simulating the discriminant functions and estimating the corresponding probabilities of misclassification. For special values of the dimensions and the covariance matrices, we obtain explicit formulas and inequalities for the probabilities of misclassification. We apply these results to data given by Stocks (1933) in a study of the physical characteristics of twin children, and to data provided by Rencher (1995) in a study of the relationship between football helmet design and neck injuries. For each application, we estimate the exact probabilities of misclassification, and in the case of Stocks' data we make extensive comparisons with previously published estimates.

Friday, February, 08, 2002

3:35 - 4:35 pm

206 Cox Hall

Refreshments will be served on the second floor of Dabney Hall (left of Room 222) at 3:00 pm.