“Error Rates in Quadratic Discrimination With Constraints on the Covariance Matrices”, 1994-03-01 (; backlinks; similar):
In multivariate discrimination of several normal populations, the optimal classification procedure is based on quadratic discriminant functions.
We compare expected error rates of the quadratic classification procedure if the covariance matrices are estimated under the following 4 models: (1) arbitrary covariance matrices, (2) common principal components, (3) proportional covariance matrices, and (4) identical covariance matrices.
Using Monte Carlo simulation to estimate expected error rates, we study the performance of the 4 discrimination procedures for 5 different parameter setups corresponding to “standard” situations that have been used in the literature. The procedures are examined for sample sizes ranging 10–60, and for 2 to 4 groups.
Our results quantify the extent to which a parsimonious method reduces error rates, and demonstrate that choosing a simple method of discrimination is often beneficial even if the underlying model assumptions are wrong.
[Keywords: Common principal components, Linear Discriminant Function, Monte Carlo simulation, Proportional Covariance Matrices]