On the Consistency and Large Deviations of the Method of Empirical Means in Stochastic Programming Problems

Knopov, P., Ermolieva, T., & Kasitskaya, E. (2025). On the Consistency and Large Deviations of the Method of Empirical Means in Stochastic Programming Problems. In: Theory, Algorithms, and Experiments in Applied Optimization: In Honor of the 70th Birthday of Panos Pardalos. Eds. Goldengorin, B., pp. 151-170 Cham, Switzerland: Springer. ISBN 978-3-031-91356-3 10.1007/978-3-031-91357-0_8.

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Abstract

The article presents a series of results concerning the empirical means method of stochastic optimization theory. The main attention is given to the study of the asymptotic behavior of empirical estimates and their convergence rate via large deviation theory for models with independent or weakly dependent random variables satisfying the strong mixing conditions. Models with discrete or continuous one-dimensional and multidimensional arguments are considered. Examples demonstrate the connection between the empirical means method and the methods of regression analysis and risk theory. The possibilities of using the empirical means method to solve a wide range of applied problems are indicated.

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