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Asymptotic Theory of Nonlinear Regression

  • Alexander V. Ivanov

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

Table of contents

  1. Front Matter
    Pages i-vi
  2. Alexander V. Ivanov
    Pages 1-3
  3. Alexander V. Ivanov
    Pages 5-78
  4. Alexander V. Ivanov
    Pages 79-153
  5. Alexander V. Ivanov
    Pages 251-288
  6. Back Matter
    Pages 289-330

About this book

Introduction

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 ().

Keywords

Estimator Parameter Power Probability theory linear regression modeling normal distribution regression systems theory

Authors and affiliations

  • Alexander V. Ivanov
    • 1
  1. 1.Glushkov Institute for CyberneticsKievUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8877-5
  • Copyright Information Springer Science+Business Media B.V. 1997
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4775-5
  • Online ISBN 978-94-015-8877-5
  • Buy this book on publisher's site
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