Estimation of classification error

This paper discusses methods of estimating the probability of error for the Bayes´ classifier which must be designed and tested with a finite number of classified samples. The expected difference between estimators is discussed. A simplified algorithm to compute Lachenbruch´s method is proposed for multivariate normal distributions with unequal covariance matrices. Also, the variances of the likelihood ratios are given so as to compare them with the differences between the estimates. The discussion is extended to nonparametric classifiers by using the Parzen approximation for the density functions. Experimental results are shown for both parametric and nonparametric cases.