Investigation and optimisation of Rosenblatt–Parsen classifier with the aid of asymptotic expansions

The paper is concerned with a learning classifier of multidimensional observations where Rosenblatt–Parsen estimates are used for observation probability distribution densities. An approximate expression is obtained for the risk (mean losses) of the classification as a function of training sample sizes. With the rist at its minimal, the optimal values of the classifier parameters (fuzziness coefficients) are found. Numerical examples are given.