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Asymptotic Theory of Nonlinear Regression : Nonconvex Optimization and Its Applications - A. V. Ivanov

Asymptotic Theory of Nonlinear Regression

Nonconvex Optimization and Its Applications

Hardcover Published: 30th November 1996
ISBN: 9780792343356
Number Of Pages: 330

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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. The text 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.

Introductionp. 1
Consistencyp. 5
Introductory Remarksp. 5
Large Deviations of the Least Squares Estimator in the Case of Errors Having an Exponential Momentp. 9
Large Deviations of the Least Squares Estimator in the Case of Errors with a Moment of Finite Orderp. 25
The Differentiability of Regression Functions and the Consistency of the Least Squares Estimatorp. 45
Strong Consistencyp. 58
Taking the Logarithm of Non-Linear Modelsp. 73
Approximation by a Normal Distributionp. 79
Stochastic Asymptotic Expansion of Least Squares Estimatorsp. 79
Asymptotic Normality of Least Squares Estimators: First Resultsp. 92
Asymptotic Normality of Least Moduli Estimatorsp. 108
Asymptotic Expansion of the Distribution of Least Squares Estimatorsp. 119
Calculation of First Polynomials of an Asymptotic Expansion of the Distribution of a Least Squares Estimatorp. 144
Asymptotic Expansions Related to the Least Squares Estimatorp. 155
Asymptotic Expansion of Least Squares Estimator Momentsp. 155
Asymptotic Expansions Related to the Estimator of the Variance of Errors of Observationp. 168
Asymptotic Expansion of the Distribution of the Variance Estimator of Observational Error in Gaussian Regressionp. 188
Jack Knife and Cross-Validation Methods of Estimation of the Variance of Errors of Observationp. 196
Asymptotic Expansions of Distributions of Quadratic Functionals of the Least Squares Estimatorp. 207
Comparison of Powers of a Class of Tests of Hypotheses on a Non-Linear Regression Parameterp. 229
Geometric Properties of Asymptotic Expansionsp. 251
Certain Aspects of the Differential Geometry of Models of Non-Linear Regressionp. 251
The Geometric Interpretation of Asymptotic Expansionsp. 276
Subsidiary Factsp. 289
List of Principal Notationsp. 298
Commentaryp. 303
Bibliographyp. 309
Indexp. 325
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792343356
ISBN-10: 0792343352
Series: Nonconvex Optimization and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 330
Published: 30th November 1996
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.06
Weight (kg): 0.65