COMPARING OPTIMISM OF ERROR RATE ESTIMATORS IN DISCRIMINANT ANALYSIS BY MONTE CARLO SIMULATION ON MULTIVARIATE NORMAL DATA

I W. MANGKU (Bogor Agricultural University)

Milang Journal of Mathematics and Its Applications
Vol. 9 No. 2 (2010): Journal of Mathematics and Its Applications

The problem considered in this paper is estimation of the error rate in two-group discriminant analysis. Here, performance of 19 existing error rate estimators are compared and contrasted by mean of Monte Carlo simulations under the ideal condition that both parent populations are multivariate normal with common covariance matrix. The criterion used for comparing those error rate estimators is optimism. Five experimental factors are considered for the simulation, they are the number of variables, the sample size relative to the number of variables, the Mahalanobis squared distance between the two populations, dependency factor among variables, and the degree of variation among the elements of the mean vector of the populations. The result of the simulation shows that there is no estimator performing the best for all situations. However, in general, the estimator U¹ proposed by Lachenbruch and Mickey (1968) is the best