Asymptotic Theory of Nonlinear Regression by A.A. IvanovAsymptotic Theory of Nonlinear Regression by A.A. Ivanov

Asymptotic Theory of Nonlinear Regression

byA.A. Ivanov

Paperback | December 6, 2010

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This book presents up-to-date mathematical results in asymptotic theory on nonlinear regression on the basis of various asymptotic expansions of least squares, its characteristics, and its distribution functions of functionals of Least Squares Estimator. It is divided into four chapters. In Chapter 1 assertions on the probability of large deviation of normal Least Squares Estimator of regression function parameters are made. Chapter 2 indicates conditions for Least Moduli Estimator asymptotic normality. An asymptotic expansion of Least Squares Estimator as well as its distribution function are obtained and two initial terms of these asymptotic expansions are calculated. Separately, the Berry-Esseen inequality for Least Squares Estimator distribution is deduced. In the third chapter asymptotic expansions related to functionals of Least Squares Estimator are dealt with. Lastly, Chapter 4 offers a comparison of the powers of statistical tests based on Least Squares Estimators. The Appendix gives an overview of subsidiary facts and a list of principal notations. Additional background information, grouped per chapter, is presented in the Commentary section. The volume concludes with an extensive Bibliography. Audience: This book will be of interest to mathematicians and statisticians whose work involves stochastic analysis, probability theory, mathematics of engineering, mathematical modelling, systems theory or cybernetics.
Title:Asymptotic Theory of Nonlinear RegressionFormat:PaperbackDimensions:336 pages, 9.25 × 6.1 × 0 inPublished:December 6, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048147751

ISBN - 13:9789048147755

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Table of Contents

Introduction. 1. Consistency. 2. Approximation by a Normal Distribution. 3. Asymptotic Expansions Related to the Least Squares Estimator. 4. Geometric Properties of Asymptotic Expansions. Appendix: I: Subsidiary Facts. II: List of Principal Notations. Commentary. Bibliography. Index.