Statistical Inference for Spatial Poisson Processes
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Home > Mathematics and Science Textbooks > Mathematics > Probability and statistics > Statistical Inference for Spatial Poisson Processes: (134 Lecture Notes in Statistics)
Statistical Inference for Spatial Poisson Processes: (134 Lecture Notes in Statistics)

Statistical Inference for Spatial Poisson Processes: (134 Lecture Notes in Statistics)


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About the Book

The book discusses the estimation theory for the wide class of inhomogeneous Poisson processes. The consistency, limit distributions and the convergence of moments of parameter estimators are established in regular and non-regular (change-point type) problems. The maximum likelihood, Bayesian, and the minimum distance estimators are investigated in parametric problems and the empiric intensity measure and the kernel-type estimators are studied in nonparametric estimation problems. The properties of the estimators are also described in the situations when the observed Poisson process does not belong to the parametric family (no true model), when there are many true models (nonidentifiable family), when the observation window can be chosen by an optimal way, and others. The question of asymptotic efficiency of estimators is discussed in all of these problems. The book will be useful for those who use models of Poisson processes in their research. The large number of examples of inhomogeneous Poisson processes discussed in the book are taken from the fields of optical communications, reliability, image processing, and nuclear medicine. The material is suitable for graduate courses on stochastic processes. The book assumes familiarity with probability theory and mathematical statistics. Yury A. Kutoyants, Professor of Mathematics at the University of Main, Le Mans, France, is a member of the Bernoulli Society, the Mathematical Society of France, and the Institute of Mathematical Statistics. He is associate editor of "Finance and Stochastics" and "Statistical Inference for Stochastic Processes." He is author of "Parameter Estimation for Stochastic Processes" (Heldermann Verlag, Berlin, 1984) and "Identification of Dynamical Systems with Small Noise" (Kluwer, Dordrecht, 1994), and the of about 70 articles on the

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.


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Product Details
  • ISBN-13: 9780387985626
  • Publisher: Springer-Verlag New York Inc.
  • Publisher Imprint: Springer-Verlag New York Inc.
  • Height: 235 mm
  • No of Pages: 279
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 038798562X
  • Publisher Date: 11 Sep 1998
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 134 Lecture Notes in Statistics


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Statistical Inference for Spatial Poisson Processes: (134 Lecture Notes in Statistics)
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