Statistical Inference for Spatial Proces
β B.D.Ripley
π Library
π
1988
π Cambridge University Press
π English
β¦ LIBER β¦
π
Statistical Inference for Spatial Poisson Processes
β Scribed by Yu. A. Kutoyants (auth.)
- Publisher
- Springer-Verlag New York
- Year
- 1998
- Tongue
- English
- Leaves
- 281
- Series
- Lecture Notes in Statistics 134
- Edition
- 1
- Category
- Library
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β¦ Synopsis
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 particΒ 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 PoisΒ 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 enΒ gineering problems and the existing computing algorithms are sufficiently powerful to calculate these estimators. Therefore the properties of estimators can be interesting too.
β¦ Table of Contents
Front Matter....Pages N2-vii
Introduction....Pages 1-15
Auxiliary Results....Pages 17-43
First Properties of Estimators....Pages 45-97
Asymptotic Expansions....Pages 99-142
Nonstandard Problems....Pages 143-181
The Change-Point Problems....Pages 183-224
Nonparametric Estimation....Pages 225-250
Back Matter....Pages 251-278
β¦ Subjects
Statistics, general
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