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Statistical Inference for Spatial Poisson Processes

  • Book
  • © 1998

Overview

Authors:
  1. Yu. A. Kutoyants

    1. Laboratoire de Statistique et Processus, Université du Maine, Le Mans, France

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Part of the book series: Lecture Notes in Statistics (LNS, volume 134)

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Table of contents (7 chapters)

  1. Front Matter

    Pages N2-vii
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  2. Introduction

    • Yu. A. Kutoyants
    Pages 1-15

  3. Auxiliary Results

    • Yu. A. Kutoyants
    Pages 17-43

  4. First Properties of Estimators

    • Yu. A. Kutoyants
    Pages 45-97

  5. Asymptotic Expansions

    • Yu. A. Kutoyants
    Pages 99-142

  6. Nonstandard Problems

    • Yu. A. Kutoyants
    Pages 143-181

  7. The Change-Point Problems

    • Yu. A. Kutoyants
    Pages 183-224

  8. Nonparametric Estimation

    • Yu. A. Kutoyants
    Pages 225-250

  9. Back Matter

    Pages 251-278
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Keywords

About this book

This work is devoted to several problems of parametric (mainly) and nonparametric estimation through the observation of Poisson processes defined on general spaces. Poisson processes are quite popular in applied research and therefore they attract the attention of many statisticians. There are a lot of good books on point processes and many of them contain chapters devoted to statistical inference for general and partic­ ular models of processes. There are even chapters on statistical estimation problems for inhomogeneous Poisson processes in asymptotic statements. Nevertheless it seems that the asymptotic theory of estimation for nonlinear models of Poisson processes needs some development. Here nonlinear means the models of inhomogeneous Pois­ son processes with intensity function nonlinearly depending on unknown parameters. In such situations the estimators usually cannot be written in exact form and are given as solutions of some equations. However the models can be quite fruitful in en­ gineering problems and the existing computing algorithms are sufficiently powerful to calculate these estimators. Therefore the properties of estimators can be interesting too.

Authors and Affiliations

  • Laboratoire de Statistique et Processus, Université du Maine, Le Mans, France

    Yu. A. Kutoyants

Bibliographic Information

  • Book Title: Statistical Inference for Spatial Poisson Processes

  • Authors: Yu. A. Kutoyants

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-1706-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Softcover ISBN: 978-0-387-98562-6Published: 11 September 1998

  • eBook ISBN: 978-1-4612-1706-0Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VIII, 279

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes, Applications of Mathematics

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