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" Empirical Estimates in Stochastic Optimization and Identification "
by Pavel S. Knopov, Evgeniya J. Kasitskaya.
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BL
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621341
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dltt
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| Main Entry
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Knopov, Pavel S.
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| Title & Author
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Empirical Estimates in Stochastic Optimization and Identification\ by Pavel S. Knopov, Evgeniya J. Kasitskaya.
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| Publication Statement
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Boston, MA :: Springer US :: Imprint: Springer,, 2002.
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| Series Statement
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Applied Optimization,; 71
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| ISBN
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9781475735673
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: 9781441952240
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| Contents
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1 Introduction -- 2 Parametric Empirical Methods -- 3 Parametric Regression Models -- 4 Periodogram Estimates for Random Processes and Fields -- 5 Nonparametric Identification Problems -- References.
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| Abstract
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One of the basic problems of statistical investigation is taking the best in some sense decision by observations of some totality of data. In this book empir ical methods for solving of stochastic optimization problems and identification methods closely connected with them are investigated. The main attention is paid to studying of asymptotic behavior of the estimates, proving of the asser tions about tending of the considered estimates to optimal ones under unlimited increase of the sample size. The sufficiently complete idea on empirical methods in the theory of optim ization and estimation can be found in the monographs of Ibragimov and Has'minskii [52], Ermoliev and Wets [105], van de Geer [30], Pfanzagl and We felmeyer [107] and many others where the new approach to the investigation for discrete and continuous observations is considered. In the present work some new parametric problems of stochastic optimiza tion and estimation are investigated, the sufficient attention is paid to non parametric problems and continuous models with a multidimensional argument. The first chapter is auxiliary. The second one is devoted to investigation of empirical estimates in stochastic optimization problems. In the third chapter parametric regression models are considered, the connection between some of these problems and stochastic optimization problems being studied in the pre vious chapter is indicated. The fourth chapter is devoted to studying of so-called periodogram estimates.
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Statistics.
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Systems theory.
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Mathematical optimization.
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Distribution (Probability theory).
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Kasitskaya, Evgeniya J.
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SpringerLink (Online service)
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