Asymptotic Optimal Inference For Non Ergodic Models
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Asymptotic Optimal Inference For Non Ergodic Models
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Author : Ishwar V. Basawa
language : en
Publisher:
Release Date : 1983
Asymptotic Optimal Inference For Non Ergodic Models written by Ishwar V. Basawa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Asymptotic efficiencies (Statistics) categories.
Asymptotic Optimal Inference For Non Ergodic Models
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Author : I. V Basawa
language : en
Publisher:
Release Date : 1983-02-07
Asymptotic Optimal Inference For Non Ergodic Models written by I. V Basawa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-02-07 with categories.
Asymptotic Optimal Inference For Non Ergodic Models
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Author : I. V. Basawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Optimal Inference For Non Ergodic Models written by I. V. Basawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph contains a comprehensive account of the recent work of the authors and other workers on large sample optimal inference for non-ergodic models. The non-ergodic family of models can be viewed as an extension of the usual Fisher-Rao model for asymptotics, referred to here as an ergodic family. The main feature of a non-ergodic model is that the sample Fisher information, appropriately normed, converges to a non-degenerate random variable rather than to a constant. Mixture experiments, growth models such as birth processes, branching processes, etc. , and non-stationary diffusion processes are typical examples of non-ergodic models for which the usual asymptotics and the efficiency criteria of the Fisher-Rao-Wald type are not directly applicable. The new model necessitates a thorough review of both technical and qualitative aspects of the asymptotic theory. The general model studied includes both ergodic and non-ergodic families even though we emphasise applications of the latter type. The plan to write the monograph originally evolved through a series of lectures given by the first author in a graduate seminar course at Cornell University during the fall of 1978, and by the second author at the University of Munich during the fall of 1979. Further work during 1979-1981 on the topic has resolved many of the outstanding conceptual and technical difficulties encountered previously. While there are still some gaps remaining, it appears that the mainstream development in the area has now taken a more definite shape.
Asymptotic Theory Of Statistical Inference For Time Series
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Author : Masanobu Taniguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Theory Of Statistical Inference For Time Series written by Masanobu Taniguchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Higher Order Asymptotic Theory For Time Series Analysis
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Author : Masanobu Taniguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Higher Order Asymptotic Theory For Time Series Analysis written by Masanobu Taniguchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.
Rabi N Bhattacharya
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Author : Manfred Denker
language : en
Publisher: Birkhäuser
Release Date : 2016-06-30
Rabi N Bhattacharya written by Manfred Denker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Mathematics categories.
This volume presents some of the most influential papers published by Rabi N. Bhattacharya, along with commentaries from international experts, demonstrating his knowledge, insight, and influence in the field of probability and its applications. For more than three decades, Bhattacharya has made significant contributions in areas ranging from theoretical statistics via analytical probability theory, Markov processes, and random dynamics to applied topics in statistics, economics, and geophysics. Selected reprints of Bhattacharya’s papers are divided into three sections: Modes of Approximation, Large Times for Markov Processes, and Stochastic Foundations in Applied Sciences. The accompanying articles by the contributing authors not only help to position his work in the context of other achievements, but also provide a unique assessment of the state of their individual fields, both historically and for the next generation of researchers. Rabi N. Bhattacharya: Selected Papers will be a valuable resource for young researchers entering the diverse areas of study to which Bhattacharya has contributed. Established researchers will also appreciate this work as an account of both past and present developments and challenges for the future.
Topics In Statistical Information Theory
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Author : Solomon Kullback
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Topics In Statistical Information Theory written by Solomon Kullback and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The relevance of information theory to statistical theory and its applications to stochastic processes is a unifying influence in these TOPICS. The integral representation of discrimination information is presented in these TOPICS reviewing various approaches used in the literature, and is also developed herein using intrinsically information-theoretic methods. Log likelihood ratios associated with various stochastic processes are computed by an application of minimum discrimination information estimates. Linear discriminant functionals are used in the information-theoretic analysis of a variety of stochastic processes. Sections are numbered serially within each chapter, with a decimal notation for subsections. Equations, examples, theorems and lemmas, are numbered serially within each section with a decimal notation. The digits to the left of the decimal point represent the section and the digits to the right of the decimal point the serial number within the section. When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given. References to the bibliography are by the author's name followed by the year of publication in parentheses. The transpose of a matrix is denoted by a prime; thus one-row matrices are denoted by primes as the transposes of one-column matrices (vectors).
Robust And Nonlinear Time Series Analysis
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Author : J. Franke
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Robust And Nonlinear Time Series Analysis written by J. Franke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide~sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view be cause it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specifica tion. They have none-the-less stressed the importance of such optimali ty results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assum ed model.
Spatial Variation
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Author : B. Matern
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Spatial Variation written by B. Matern and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
This book was first published in 1960 as No. 5 of Volume 49 of Reports of the Forest Research Institute of Sweden. It was at the same time a doctor's thesis in mathematical statistics at Stockholm University. In the second edition, a number of misprints and other errors have been corrected. An author index and a subject index have been added. Finally, a new postscript comments on the later development of the subjects treated in the book. BERTIL MATERN March r¢6 Acknowledgements The completion of this thesis was facilitated through the generous assist ance of several persons and institutions. I would wish to express my sincere gratitude to my teacher, Professor HARALD CRAMtR, now chancellor of the Swedish universities, for his valuable help and encouragement. Sincere thanks are also offered to Professor ULF GRENANDER for kindly reading the first version of the manuscript and giving valuable advice. The thesis has been prepared during two widely separated periods. A preliminary draft of Ch. 2 was written in 1948, whereas the remaining parts were completed in 1959-1960. The work originates from problems which I discussed in a publication in 1947. The problems were assigned to me by Professor MANFRED NASLUND, former head of the Swedish Forest Research Institute, now governor of the province Norrbotten. It is a pleasure to acknowledge my gratefulness to Professor Naslund for his un remitting encouragement and interest in my work.
Survey Research Designs Towards A Better Understanding Of Their Costs And Benefits
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Author : Robert W. Pearson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Survey Research Designs Towards A Better Understanding Of Their Costs And Benefits written by Robert W. Pearson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
ROBERT F. BORUCH AND ROBERT W. PEARSON During the 13th Century. a vigorous argument among Middle Eastern rabbis concerned how one ought to make a fair assessment of an olive crop value for tithing purposes. Should one consolidate the crop. systematically mix the olives. and then conscientiously draw a small random sample? Or. might one simply grab a handful of olives from the nearest basket and make an estimate of the crop's worth. The issue. of course. is one that research designers and research users confront often -- balancing the need for information against the resources that must be put into actually collecting the data -- in deciding how much effort is warranted to produce fair evidence. For the rabbis. who argued for twenty-five years over the matter. the issue can be resolved with a special rule. In this as in other cases. if the demand for information is biblical in origin -- if God is its source. then one ought to be considerably conscientious; a more scientific and more expensive endeavor is warranted. We may at times subscribe to this kind of rule of thumb in determining what quality of information is warranted under what conditions. But other rules and approaches are possible. And as medieval Jewish. Arabic. and Christian philosophy suggests. the alternatives need to be thought out and tested. Our interest is a bit more contemporary but has some spiritual kinship with early scholars' interest in empirical evidence.