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The Theory and Applications of Statistical Inference Functions

  • D. L. McLeish
  • Christopher G. Small

Part of the Lecture Notes in Statistics book series (LNS, volume 44)

Table of contents

  1. Front Matter
    Pages i-vi
  2. D. L. McLeish, Christopher G. Small
    Pages 1-12
  3. D. L. McLeish, Christopher G. Small
    Pages 13-36
  4. D. L. McLeish, Christopher G. Small
    Pages 37-56
  5. D. L. McLeish, Christopher G. Small
    Pages 57-73
  6. D. L. McLeish, Christopher G. Small
    Pages 88-112
  7. Back Matter
    Pages 113-128

About this book

Introduction

This monograph arose out of a desire to develop an approach to statistical infer­ ence that would be both comprehensive in its treatment of statistical principles and sufficiently powerful to be applicable to a variety of important practical problems. In the latter category, the problems of inference for stochastic processes (which arise com­ monly in engineering and biological applications) come to mind. Classes of estimating functions seem to be promising in this respect. The monograph examines some of the consequences of extending standard concepts of ancillarity, sufficiency and complete­ ness into this setting. The reader should note that the development is mathematically "mature" in its use of Hilbert space methods but not, we believe, mathematically difficult. This is in keeping with our desire to construct a theory that is rich in statistical tools for infer­ ence without the difficulties found in modern developments, such as likelihood analysis of stochastic processes or higher order methods, to name but two. The fundamental notions of orthogonality and projection are accessible to a good undergraduate or beginning graduate student. We hope that the monograph will serve the purpose of enriching the methods available to statisticians of various interests.

Keywords

Censoring Likelihood Martingale Median Stochastic processes stochastic process

Authors and affiliations

  • D. L. McLeish
    • 1
  • Christopher G. Small
    • 1
  1. 1.Department of Statistics and Actuarial ScienceUniversity of WaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3872-0
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96720-2
  • Online ISBN 978-1-4612-3872-0
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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