Statistical Inference for Spatial Poisson Processes
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...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1998, 1998
|
| Edition: | 1st ed. 1998 |
| Series: | Lecture Notes in Statistics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Auxiliary Results
- 1.1 Poisson process
- 1.2 Estimation problems
- 2 First Properties of Estimators
- 2.1 Asymptotic of the maximum likelihood and Bayesian estimators
- 2.2 Minimum distance estimation
- 2.3 Special models of Poisson processes
- 3 Asymptotic Expansions
- 3.1 Expansion of the MLE
- 3.2 Expansion of the Bayes estimator
- 3.3 Expansion of the minimum distance estimator
- 3.4 Expansion of the distribution functions
- 4 Nonstandard Problems
- 4.1 Misspecified model
- 4.2 Nonidentifiable model
- 4.3 Optimal choice of observation windows
- 4.4 Optimal choice of intensity function
- 5 The Change-Point Problems
- 5.1 Phase and frequency estimation
- 5.2 Chess-field problem
- 5.3 Top-hat problem
- 6 Nonparametric Estimation
- 6.1 Intensity measure estimation
- 6.2 Intensity function estimation
- Remarks