Speciality:
01.01.05 (Probability theory and mathematical statistics)
Birth date:
25.12.1952
E-mail: ,
Keywords: mathematical statistics; inverse problems; asymptotic methods of statistics; nonparametric hypothesis testing; large deviations; sequential estimation; sufficient statistics.
Subject:
The asymptotic structure of nonregular statistical experiments was investigated. The structure of minimal sufficient statistics was studied in multivariate case and in the case of discontinuous densities. The asymptotically minimax estimators have been found in deconvolution problems. The relation of rates of convergence in minimax and Bayes settings has been investigated. The optimality of rates of convergence of Tikhonov regularizing algorithm has been shown in stochastic setting. The necessary and sufficient conditions of distinguishability of sets of hypothesis and alternatives in $L_2$ was obtained. The asymptotically minimax tests were obtained in the problem of testing hypothesis in $L_2$ if the sets of alternatives are ellipsoid in $L_2$ with the balls in $L_2$ deleted. The asymptotic minimaxity of tests of Kolmogorov, omega-squared and chi-squared types was proved under natural nonparametric sets of alternatives. The lower bounds for probabilities of large deviations of tests and estimators were proved under assumptions that almost can not be improved.
Main publications:
Ermakov M. S. On distinguishability of two nonparametric sets of hypothesis // Statist. Probab. Lett., 2000, v. 48, p. 275–282.
Ermakov M. S. Minimax estimation in a deconvolution problem // J. of Phys. Ser. A Math. Gen., 1992, v. 25, p. 1273–1282.
