Empirical estimates in stochastic optimization and identification随机优化与识别的经验估计

作者简介

　　This book contains problems of stochastic optimization and identification. Results concerning uniform law of large numbers, convergence of approximate estimates of extremal points, as well as empirical estimates of functionals with probability 1 and in probability are presented. It is shown that the investigation of asymptotic properties of approximate estimates and estimates of unknown parameters in various regression models can be carried out by using general methods, which are presented by the authors. The connection between stochastic programming methods and estimation theory is described. It was assumed to use the methods of asymptotic stochastic analysis for investigation of extremal points, and on the other hand to use stochastic programming methods to find optimal estimates. 　　Audience: Specialists in stochastic optimization and estimations, postgraduate students, and graduate students studying such topics.

书籍目录

PREFACE1 INTRODUCTION2 PARAMETRIC EMPIRICAL METHODS  2.1  Auxiliary Results  2.2  Models with Independent Observations  2.3  Models with Continuous Time  2.4  Models with Restrictions in the Form of Inequalities  2.5  Nonstationary Empirical Estimates3 PARAMETRIC REGRESSION MODELS  3.1  Estimates of the Parameters for Gaussian Regression Mod-els with Discrete Time  3.2  Estimates of the Parameters for Gaussian Random Field with a Continuous Argument  3.3  Nonstationary Regression Model for Gaussian Field  3.4  Identification of the Parameters for the Stationary Nonlin-ear Regression as a Special Case of Stochastic Programming Problem  3.5  Nonstationary Regression Model for a Random Field Ob-served in a Circle  3.6  Gaussian Regression Models for Quasistationary RandomProcesses4 PERIODOGRAM ESTIMATES FOR RANDOM PROCESSES AND FIELDS  4.1  Preliminary Results  4.2  Asymptotic Behavior of Periodogram Estimates of the First Type  4.3  Asymptotic Behavior of Periodogram Estimates of the Second Type  4.4  Periodogram Estimates in Rm5 NONPARAMETRIC IDENTIFICATION PROBLEMS  5.1  The Investigation of the General Problem  5.2  The Nonparametric Regression Model with Observations in a Finite Number of Curves on the Plane  5.3  The Nonparametric Regression Model with Observations in Nodes of a Rectangle  5.4  The Periodical Signal Estimation by Observation of Its Mix- ture with Homogeneous Random FieldREFERENCES

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