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Asymptotic Theory of Nonlinear Regression

  • Book
  • © 1997

Overview

Authors:
  1. Alexander V. Ivanov

    1. Glushkov Institute for Cybernetics, Kiev, Ukraine

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Part of the book series: Mathematics and Its Applications (MAIA, volume 389)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-vi
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  2. Introduction

    • Alexander V. Ivanov
    Pages 1-3

  3. Consistency

    • Alexander V. Ivanov
    Pages 5-78

  4. Approximation by a Normal Distribution

    • Alexander V. Ivanov
    Pages 79-153

  5. Asymptotic Expansions Related to the Least Squares Estimator

    • Alexander V. Ivanov
    Pages 155-250

  6. Geometric Properties of Asymptotic Expansions

    • Alexander V. Ivanov
    Pages 251-288

  7. Back Matter

    Pages 289-330
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Keywords

About this book

Let us assume that an observation Xi is a random variable (r.v.) with values in 1 1 (1R1 , 8 ) and distribution Pi (1R1 is the real line, and 8 is the cr-algebra of its Borel subsets). Let us also assume that the unknown distribution Pi belongs to a 1 certain parametric family {Pi() , () E e}. We call the triple £i = {1R1 , 8 , Pi(), () E e} a statistical experiment generated by the observation Xi. n We shall say that a statistical experiment £n = {lRn, 8 , P; ,() E e} is the product of the statistical experiments £i, i = 1, ... ,n if PO' = P () X ... X P () (IRn 1 n n is the n-dimensional Euclidean space, and 8 is the cr-algebra of its Borel subsets). In this manner the experiment £n is generated by n independent observations X = (X1, ... ,Xn). In this book we study the statistical experiments £n generated by observations of the form j = 1, ... ,n. (0.1) Xj = g(j, (}) + cj, c c In (0.1) g(j, (}) is a non-random function defined on e , where e is the closure in IRq of the open set e ~ IRq, and C j are independent r. v .-s with common distribution function (dJ.) P not depending on ().

Authors and Affiliations

  • Glushkov Institute for Cybernetics, Kiev, Ukraine

    Alexander V. Ivanov

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