Effect of intraclass correlation among training samples on the misclassification probabilities of bayes procedure

Abstract

The sample mean and sample covariance matrix are unbiased and consistent estimates of population mean and covariance matrix only if the samples are independent. In practical applications of Bayes' procedure these estimates are used in place of population means and covariance matrices on the assumption of independence among the training samples. This practice has often given, especially in remote sensing data analysis, misclassification probabilities much higher than that can be accounted for theoretically. The reason may be that the assumption of independence may not be valid. In reality, the samples are rarely independent, they are rather dependent, at best equicorrelated. This paper investigates how such intraclass correlation among the training samples affects the misclassification probabilities of the Bayes' procedure.