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

Author

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  • Pavel Knopov

    (National Academy of Sciences of Ukraine)

  • Tatiana Ermolieva

    (International Institute for Applied Systems Analysis)

  • Evgeniya Kasitskaya

    (National Academy of Sciences of Ukraine)

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.

Suggested Citation

  • Pavel Knopov & Tatiana Ermolieva & Evgeniya Kasitskaya, 2025. "On the Consistency and Large Deviations of the Method of Empirical Means in Stochastic Programming Problems," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-3-031-91357-0_8
    DOI: 10.1007/978-3-031-91357-0_8
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