Smoothed additive estimators for non-error rates in multiple discriminant analysis

摘要

A generalization of smoothed additive estimators for non-error rates to the case of more than two groups is discussed. Several properties the smoothing should have are shown to be satisfied. The problem of choosing a smoothing parameter is considered and a parameter choice depending on the sample is proposed. In simulation experiments with normal, uniform and discrete distributions the smoothed additive estimators with fixed and variable smoothing parameter are compared to the leaving-one out method and the resubstitution method with respect to bias and variance.