Classification of a screened data into one of two normal populations perturbed by a screening scheme

In normal classification analysis, there may be cases where the population distributions are perturbed by a screening scheme. This paper considers a new classification method for screened data that is obtained from the perturbed normal distributions. Properties of each population distribution is considered and the best region for classifying the screened data is obtained. These developments yield yet another optimal rule for the classification. The rule is studied from several aspects such as a linear approximation, error rates, and estimation of the rule using the EM algorithm. Relationships among these aspects as well as investigation of the rule’s performance are also considered. The screened classification ideas are illustrated in detail using numerical examples.