This book contains papers presented at the Seminar on Mathematical Statistics held at the Institute for Problems of Information Transmission of the Academy of Sciences in the former Soviet Union. Founded in the mid-1960s, this seminar is still active today and attracts most of the researchers in Moscow who are interested in mathematical statistics. The topics covered include density, regression, and image estimation, adaptive estimation, stochastic approximation, median estimation, sequential experimental design, and large deviations for empirical measures. This collection is distinguished by the high scientific level of the papers and their modern approach. This book will be of interest to scientists and engineers who use probability and statistics, to mathematicians and applied statisticians who work in approximation theory, and to computer scientists who work in image analysis.
Lower bound for the integral risk of density function estimates by A. Samarov On nonparametric estimation of functions satisfying differential inequalities by A. S. Nemirovskii Asymptotically minimax image reconstruction problems by A. P. Korostelev and A. B. Tsybakov On problems of adaptive estimation in white Gaussian noise by O. V. Lepskii On stochastic approximation with arbitrary noise (the KW-case) by B. T. Polyak and A. B. Tsybakov Pseudovalues and minimax filtering algorithms for the nonparametric median by E. N. Belitser and A. P. Korostelev On large deviations for ergodic process empirical measures by A. Yu. Veretennikov On asymptotically optimal sequential experimental design by V. G. Spokoinyi.