Regularization of the problem of hypothesis discrimination by the method of minimal errors

The paper is concerned with discrimination of statistical hypothesis on moment functions of two probabilistic measures under uncertainty. The uncertainty consists of small perturbantions in the hypotheses that are checked. The solution functional are sought in the class of Hilbert-Schmidt polynomials by minimizing the admissible error in the problem performace functional with complete information and under uncertainty. Theorems are given on conditions for existance, uniqueness, and stability of the solution functional in the hypothesis discrimination problem by the method of admissible errors. The solutioxi by the method of minimal error is shown to be Tikhonov regularized.