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.
| ISBN: | 9780387985626 |
| Publication date: | 11th September 1998 |
| Author: | Yu Kutoyants |
| Publisher: | Springer an imprint of Springer New York |
| Format: | Paperback |
| Pagination: | 276 pages |
| Series: | Lecture Notes in Statistics |
| Genres: |
Probability and statistics Stochastics Applied mathematics |
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.
Statistical Inference for Spatial Poisson Processes features in the following genres: Probability and statistics, Stochastics, Applied mathematics
Statistical Inference for Spatial Poisson Processes is available in Paperback
Statistical Inference for Spatial Poisson Processes was written by Yu Kutoyants and published by Springer an imprint of Springer New York
Statistical Inference for Spatial Poisson Processes has 276 pages
Yes it is part of Lecture Notes in Statistics series