Empirical Estimates in Stochastic Optimization and Identification

✍ Scribed by Pavel S. Knopov, Evgeniya J. Kasitskaya (auth.)

• Publisher: Springer US
• Year: 2002
• Tongue: English
• Leaves: 255
• Series: Applied Optimization 71
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-viii
Introduction....Pages 1-9
Parametric Empirical Methods....Pages 11-70
Parametric Regression Models....Pages 71-162
Periodogram Estimates for Random Processes and Fields....Pages 163-197
Nonparametric Identification Problems....Pages 199-237
Back Matter....Pages 239-250

✦ Subjects

Statistics, general; Systems Theory, Control; Optimization; Probability Theory and Stochastic Processes