Classification of Random Series of Unknown Length

The author considers the problem of classification of multivariate random observations in the situation in which the sequence of true numbers of classes is generated by series (or runs) of unknown length, while the distribution densities of the observations are specified to within parameters. A decision rule is constructed and investigated; this rule is based on the statistics of the homogeneity criterion and surmounts the undesirable “multiplicity effect” inherent in the rule based on the maximum-likelihood criterion.