Asymptotic Theory Of Statistical Inference For Time Series
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Asymptotic Theory of Statistical Inference for Time Series
Author: Masanobu Taniguchi
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
There has been much demand for the statistical analysis of dependent ob servations in many fields, for example, economics, engineering and the nat ural sciences. A model that describes the probability structure of a se ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual autoregressive (AR), moving average (MA), and autoregressive moving average (ARMA) processes. We deal with a wide variety of stochastic processes, for example, non-Gaussian linear processes, long-memory processes, nonlinear processes, orthogonal increment process es, and continuous time processes. For them we develop not only the usual estimation and testing theory but also many other statistical methods and techniques, such as discriminant analysis, cluster analysis, nonparametric methods, higher order asymptotic theory in view of differential geometry, large deviation principle, and saddlepoint approximation. Because it is d ifficult to use the exact distribution theory, the discussion is based on the asymptotic theory. Optimality of various procedures is often shown by use of local asymptotic normality (LAN), which is due to LeCam. This book is suitable as a professional reference book on statistical anal ysis of stochastic processes or as a textbook for students who specialize in statistics. It will also be useful to researchers, including those in econo metrics, mathematics, and seismology, who utilize statistical methods for stochastic processes.
Asymptotic Theory of Statistics and Probability
Author: Anirban DasGupta
language: en
Publisher: Springer Science & Business Media
Release Date: 2008-03-07
This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
Asymptotics in Statistics
Author: Lucien Le Cam
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
by Sara van de Geer. Also, we did not include material due to David Donoho, lain Johnstone, and their school. We found our selves unprepared to write a distillate of the material. We did touch briefly on "nonparametrics," but not on "semiparamet rics." This is because we feel that the semiparametric situation has not yet been properly structured. We hope that the reader will find this book interesting and challenging, in spite of its shortcomings. The material was typed in LaTeX form by the authors them selves, borrowing liberally from the 1990 script by Chris Bush. It was reviewed anonymously by distinguished colleagues. We thank them for their kind encouragement. Very special thanks are due to Professor David Pollard who took time out of a busy schedule to give us a long list of suggestions. We did not follow them all, but we at least made attempts. We wish also to thank the staff of Springer-Verlag for their help, in particular editor John Kimmel, who tried to make us work with all deliberate speed. Thanks are due to Paul Smith, Te-Ching Chen and Ju-Yi-Yen, who helped with the last-minute editorial corrections.