Investigation of risk for statistical classifiers using minimum contrast estimators

Let the dimension of observational space is fixed, the size of the classified sample increases and the densities of observations are regular. We construct an asymptotic expansion of risk for the family of classifiers («plug-in rule» type) using minimum contrast (MC) estimators; this expansion is based on Chibisov's expansion for MC-estimators. The formulas for the approximate risk evaluation as a functions of sample sizes are obtained and investigated. The minimum of the main terms in the risk expansion is proved to correspond to the maximum likelyhood estimators (in the family of MC-estimators).