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Statistical Inference for Spatial Poisson Processes

  • Yu. A. Kutoyants

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

Table of contents

  1. Front Matter
    Pages N2-vii
  2. Yu. A. Kutoyants
    Pages 1-15
  3. Yu. A. Kutoyants
    Pages 17-43
  4. Yu. A. Kutoyants
    Pages 45-97
  5. Yu. A. Kutoyants
    Pages 99-142
  6. Yu. A. Kutoyants
    Pages 143-181
  7. Yu. A. Kutoyants
    Pages 183-224
  8. Yu. A. Kutoyants
    Pages 225-250
  9. Back Matter
    Pages 251-278

About this book

Introduction

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.

Keywords

Estimator Likelihood Poisson process Probability theory Stochastic processes mathematical statistics statistics stochastic process

Authors and affiliations

  • Yu. A. Kutoyants
    • 1
  1. 1.Laboratoire de Statistique et ProcessusUniversité du MaineLe MansFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1706-0
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98562-6
  • Online ISBN 978-1-4612-1706-0
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site