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Weighted Empirical Processes in Dynamic Nonlinear Models

  • Hira L. Koul

Part of the Lecture Notes in Statistics book series (LNS, volume 166)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Hira L. Koul
    Pages 1-14
  3. Hira L. Koul
    Pages 15-68
  4. Hira L. Koul
    Pages 69-98
  5. Hira L. Koul
    Pages 99-137
  6. Hira L. Koul
    Pages 138-228
  7. Hira L. Koul
    Pages 229-293
  8. Hira L. Koul
    Pages 294-357
  9. Hira L. Koul
    Pages 358-407
  10. Hira L. Koul
    Pages 408-413
  11. Hira L. Koul
    Pages 414-425
  12. Back Matter
    Pages 427-429

About this book

Introduction

The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex­ panded version of the monograph Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph, 21 published in 1992, that includes some aspects of this development. The new inclusions are as follows. Theorems 2. 2. 4 and 2. 2. 5 give an extension of the Theorem 2. 2. 3 (old Theorem 2. 2b. 1) to the unbounded random weights case. These results are found useful in Chapters 7 and 8 when dealing with ho­ moscedastic and conditionally heteroscedastic autoregressive models, actively researched family of dynamic models in time series analysis in the 1990's. The weak convergence results pertaining to the partial sum process given in Theorems 2. 2. 6 . and 2. 2. 7 are found useful in fitting a parametric autoregressive model as is expounded in Section 7. 7 in some detail. Section 6. 6 discusses the related problem of fit­ ting a regression model, using a certain partial sum process. Inboth sections a certain transform of the underlying process is shown to provide asymptotically distribution free tests. Other important changes are as follows. Theorem 7. 3.

Keywords

boundary element method estimator fitting probability statistics

Authors and affiliations

  • Hira L. Koul
    • 1
  1. 1.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-0055-7
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95476-9
  • Online ISBN 978-1-4613-0055-7
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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