Applied Optimization

By: Pavel S. Knopov, Evgeniya J. Kasitskaya

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Hardcover | 30 June 2002

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264 Pages

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24.13 x 15.88 x 1.91

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This volume 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.

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Optimisation Game Theory Medicine Medicine in General Probability & Statistics Linear Programming

Preface	p. vii
Introduction	p. 1
Parametric Empirical Methods	p. 11
Auxiliary Results	p. 12
Models with Independent Observations	p. 19
Models with Continuous Time	p. 36
Models with Restrictions in the Form of Inequalities	p. 44
Nonstationary Empirical Estimates	p. 61
Parametric Regression Models	p. 71
Estimates of the Parameters for Gaussian Regression Models with Discrete Time	p. 72
Estimates of the Parameters for Gaussian Random Field with a Continuous Argument	p. 91
Nonstationary Regression Model for Gaussian Field	p. 115
Identification of the Parameters for the Stationary Nonlinear Regression as a Special Case of Stochastic Programming Problem	p. 133
Nonstationary Regression Model for a Random Field Observed in a Circle	p. 143
Gaussian Regression Models for Quasistationary Random Processes	p. 154
Periodogram Estimates for Random Processes and Fields	p. 163
Preliminary Results	p. 163
Asymptotic Behavior of Periodogram Estimates of the First Type	p. 174
Asymptotic Behavior of Periodogram Estimates of the Second Type	p. 186
Periodogram Estimates in R[superscript m]	p. 195
Nonparametric Identification Problems	p. 199
The Investigation of the General Problem	p. 199
The Nonparametric Regression Model with Observations in a Finite Number of Curves on the Plane	p. 210
The Nonparametric Regression Model with Observations in Nodes of a Rectangle	p. 225
The Periodical Signal Estimation by Observation of Its Mixture with Homogeneous Random Field	p. 230
References	p. 239
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Applied Optimization

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Hardcover

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