Abstract
This chapter discusses the theories and methods used in classification. It presents a general theory regarding classification into known distributions, rules based on ranks, rules based on tolerance regions, rules based on distances between empirical CDFs, nearest neighbor rules, rules with density estimates, nonparametric or distribution-free methods, classification into more than two multivariate normal populations, classification into two multivariate normal populations with different covariance matrices, compound-decision and empirical Bayes approaches, and general theory of classification when the information about the distribution is based on samples. A best-of-class or constructive rule is given by the one that optimizes certain specified criteria in a given class. The so-called nonparametric or distribution-free methods are used in statistical inference when one is concerned with a wide class of distributions that usually cannot be expressed as a parametric family with a finite number of parameters.
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