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This book is concerned with the general theory of optimal estimation of - rameters in systems subject to random e?ects and with the application of this theory. The focus is on choice of families of estimating functions, rather than the estimators derived therefrom, and on optimization within these families. Only assumptions about means and covariances are required for an initial d- cussion. Nevertheless, the theory that is developed mimics that of maximum likelihood, at least to the ?rst order of asymptotics. The term quasi-likelihood has often had a narrow interpretation, asso- ated with its application to generalized linear model type contexts, while that of optimal estimating functions has embraced a broader concept. There is, however, no essential distinction between the underlying ideas and the term quasi-likelihood has herein been adopted as the general label. This emphasizes its role in extension of likelihood based theory. The idea throughout involves ?nding quasi-scores from families of estimating functions. Then, the qua- likelihood estimator is derived from the quasi-score by equating to zero and solving, just as the maximum likelihood estimator is derived from the like- hood score.

Parameter estimation --- Parameter estimation. --- Mathematical statistics --- 519.2 --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Estimation d'un paramètre --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Applications of Mathematics. --- Estimation theory --- Stochastic systems --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics

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Stochastic processes --- Martingales (Mathematics) --- Limit theorems (Probability theory) --- Martingales (Mathématiques) --- Théorèmes limites (Théorie des probabilités) --- 519.21 --- 519.216 --- Probabilities --- Probability theory. Stochastic processes --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- 519.21 Probability theory. Stochastic processes --- Martingales (Mathématiques) --- Théorèmes limites (Théorie des probabilités)

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Stochastic processes

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This volume is dedicated to the memory of the late Professor C.C. (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist. Chris worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. He contributed significantly to this effort and took his place deservedly among the top-most rank of researchers. Throughout his career, Chris maintained also a keen interest in applications of probability and statistics, and in the history of the subject. The magnitude of his impact on his chosen area of research, both in Australia and internationally, was well recognised by the abundance of honours he received within and without the profession. The book is comprised of a number of Chris’s papers covering each one of four major topics to which he contributed. These papers are reproduced herein. The topics, and the papers in them, were selected by four of Chris’s friends and collaborators: Ishwar Basawa, Peter Hall, Ross Maller (overall Editor of the volume) and Eugene Seneta. Each topic is provided with an overview by the selecting editor. The topics cover a range of areas to which Chris made especially important contributions: Inference in Stochastic Processes, Rates of Convergence in the Central Limit Theorem, the Law of the Iterated Logarithm, and Branching Processes and Population Genetics. The Editor and the other contributors to the volume include well known researchers in probability and statistics. The collection begins with an “author’s pick” of a number of his papers which Chris considered most interesting and significant, chosen by him shortly before his death. A biography of Chris by his close friend and collaborator, Joe Gani, is also included. An introduction by the Editor and a comprehensive bibliography of Chris’s publications complete the volume. The book will be of especial interest to researchers in probability and statistics, and in the history of these subjects.

Branching processes. --- Limit theorems (Probability theory). --- Mathematical statistics. --- Probabilities. --- Stochastic processes. --- Mathematical statistics --- Probabilities --- Stochastic processes --- Branching processes --- Limit theorems (Probability theory) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Random processes --- Probability --- Statistical inference --- Statistics. --- Economics, Mathematical. --- Biomathematics. --- Econometrics. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Mathematical and Computational Biology. --- Quantitative Finance. --- Combinations --- Chance --- Least squares --- Risk --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical --- Statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics, Mathematical --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Biology --- Statistical analysis --- Statistical data --- Statistical science --- Methodology

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Mathematical statistics --- Stochastic processes --- Inference --- Processus stochastiques --- Congresses. --- Congrès