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- catalog abstract "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".
- catalog contributor b10941389.
- catalog created "1998.".
- catalog date "1998".
- catalog date "1998.".
- catalog dateCopyrighted "1998.".
- catalog description "Auxiliary Results -- First Properties of Estimators -- Asymptotic Expansions -- Nonstandard Problems -- The Change-poing Problems -- Nonparametric Estimation.".
- catalog description "Includes bibliographical references and index.".
- catalog description "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".
- catalog extent "vii, 276 p. ;".
- catalog identifier "038798562X (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in statistics (Springer-Verlag) ; v. 134.".
- catalog isPartOf "Lecture notes in statistics ; 134".
- catalog issued "1998".
- catalog issued "1998.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "519.2/3 21".
- catalog subject "Parameter estimation.".
- catalog subject "Poisson processes.".
- catalog subject "QA274.42 .K87 1998".
- catalog subject "Statistics.".
- catalog tableOfContents "Auxiliary Results -- First Properties of Estimators -- Asymptotic Expansions -- Nonstandard Problems -- The Change-poing Problems -- Nonparametric Estimation.".
- catalog title "Statistical inference for spatial Poisson processes / Yu. A. Kutoyants.".
- catalog type "text".