The work is devoted to the theory of robust parameter estimation of statistical models using the apparatus of information theory. The approach of A.M. Shurygin based on the model of a series of samples with random point contamination (point Bayesian contamination model) is considered. The first part of our work describes a non-parametric method of selecting the contamination point distribution – by maximizing Shannon entropy or cross entropy in the neighborhood of the model distribution limited by the value of Kulbak – Leibler divergence. This way of finding the distribution density of the contamination point allows us to consider the resulting estimators as robust, and, moreover, having the optimality property. We call the obtained estimators generalized radical, since their special case is the radical estimators of A.M. Shurygin.In the second part of the work, another optimal solution is obtained on the basis of the formalism of A. Rényi (or the formalism of C. Tsallis equivalent in terms of our problem) that gives a new family of estimators, the special cases of which are also some well-known estimators. To select one estimate from a family defined by different divergence constraints, an optimization approach is proposed. The main theoretical results obtained in the paper are illustrated by the example of location estimating for the cosine distribution.

parameter estimation, robustness, influence function, redescending estimators, principle of maximal entropy, Shannon entropy, Kulback – Leibler divergence, Rényi entropy, Rényi divergence, Tsallis entropy, Tsallis divergence, alpha-divergence, Burg entropy, Hellinger distance, power-of-cosine distribution.