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Weighted Empirical Processes in Dynamic Nonlinear Models

  • Book
  • © 2002

Overview

Authors:
  1. Hira L. Koul

    1. Department of Statistics and Probability, Michigan State University, East Lansing, USA

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    • Hira L. Koul
    Pages 1-14

  3. Asymptotic Properties of W.E.P.’s

    • Hira L. Koul
    Pages 15-68

  4. Linear Rank and Signed Rank Statistics

    • Hira L. Koul
    Pages 69-98

  5. M, R and Some Scale Estimators

    • Hira L. Koul
    Pages 99-137

  6. Minimum Distance Estimators

    • Hira L. Koul
    Pages 138-228

  7. Goodness-of-fit Tests in Regression

    • Hira L. Koul
    Pages 229-293

  8. Autoregression

    • Hira L. Koul
    Pages 294-357

  9. Nonlinear Autoregression

    • Hira L. Koul
    Pages 358-407

  10. Appendix

    • Hira L. Koul
    Pages 408-413

  11. Bibliography

    • Hira L. Koul
    Pages 414-425

  12. Back Matter

    Pages 427-429
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Statistics and Probability, Michigan State University, East Lansing, USA

    Hira L. Koul

Bibliographic Information

  • Book Title: Weighted Empirical Processes in Dynamic Nonlinear Models

  • Authors: Hira L. Koul

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4613-0055-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2002

  • Softcover ISBN: 978-0-387-95476-9Published: 13 June 2002

  • eBook ISBN: 978-1-4613-0055-7Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 2

  • Number of Pages: XVII, 425

  • Number of Illustrations: 1 b/w illustrations

  • Additional Information: Originally published by the Institute of Mathematical Statistics, Ohio, 1992

  • Topics: Statistical Theory and Methods

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