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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
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This book is designed for specialists needing an introduction to statistical inference in spatial statistics and its applications One of the authors themes is to show how these techniques give new insights into classical procedures including new examples in likelihood theory and newer statistical paradigms such as MonteCarlo inference and pseudolikelihood Professor Ripley also stresses the importance of edge effects and of the lack of a unique asymptotic setting in spatial problems Throughout he discusses the foundational issues posed and the difficulties both computational and philosophical which arise The final chapters consider image restoration and segmentation methods and the averaging and summarizing of images
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