Asymptotic Theory of Nonlinear Regression / Edition 1

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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 shastic analysis, probability theory, mathematics of engineering, mathematical modelling, systems theory or cybernetics.

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Product Details

  • ISBN-13: 9789048147755
  • Publisher: Springer Netherlands
  • Publication date: 12/7/2010
  • Series: Mathematics and Its Applications (closed) Series , #389
  • Edition description: Softcover reprint of hardcover 1st ed. 1997
  • Edition number: 1
  • Pages: 330
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.71 (d)

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.

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