Asymptotic Methods In Probability And Statistics

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Author: B. Szyszkowicz
Publisher: Elsevier
ISBN: 9780080499529
Size: 29.27 MB
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Asymptotic Methods In Probability And Statistics by B. Szyszkowicz


Original Title: Asymptotic Methods In Probability And Statistics

One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97. This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.

Asymptotic Methods In Probability And Statistics With Applications

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Author: N. Balakrishnan
Publisher: Springer Science & Business Media
ISBN: 1461202094
Size: 23.49 MB
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Asymptotic Methods In Probability And Statistics With Applications by N. Balakrishnan


Original Title: Asymptotic Methods In Probability And Statistics With Applications

Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.

Asymptotic Techniques For Use In Statistics

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Author: O. E. Barndorff-Nielsen
Publisher: Springer
ISBN: 9781489934253
Size: 78.65 MB
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Asymptotic Techniques For Use In Statistics by O. E. Barndorff-Nielsen


Original Title: Asymptotic Techniques For Use In Statistics

The use in statistical theory of approximate arguments based on such methods as local linearization (the delta method) and approxi mate normality has a long history. Such ideas play at least three roles. First they may give simple approximate answers to distributional problems where an exact solution is known in principle but difficult to implement. The second role is to yield higher-order expansions from which the accuracy of simple approximations may be assessed and where necessary improved. Thirdly the systematic development of a theoretical approach to statistical inference that will apply to quite general families of statistical models demands an asymptotic formulation, as far as possible one that will recover 'exact' results where these are available. The approximate arguments are developed by supposing that some defining quantity, often a sample size but more generally an amount of information, becomes large: it must be stressed that this is a technical device for generating approximations whose adequacy always needs assessing, rather than a 'physical' limiting notion. Of the three roles outlined above, the first two are quite close to the traditional roles of asymptotic expansions in applied mathematics and much ofthe very extensive literature on the asymptotic expansion of integrals and of the special functions of mathematical physics is quite directly relevant, although the recasting of these methods into a probability mould is quite often enlightening.

Asymptotic Methods In Statistical Decision Theory

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Author: Lucien Le Cam
Publisher: Springer Science & Business Media
ISBN: 1461249465
Size: 72.16 MB
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Asymptotic Methods In Statistical Decision Theory by Lucien Le Cam


Original Title: Asymptotic Methods In Statistical Decision Theory

This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called "experiments" and "transitions" between them. An "experiment" is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process.

Expansions And Asymptotics For Statistics

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Author: Christopher G. Small
Publisher: CRC Press
ISBN: 9781420011029
Size: 39.71 MB
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Expansions And Asymptotics For Statistics by Christopher G. Small


Original Title: Expansions And Asymptotics For Statistics

Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. The book first discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, and the study of rational approximations to functions. With a focus on asymptotic normality and asymptotic efficiency of standard estimators, it covers various applications, such as the use of the delta method for bias reduction, variance stabilisation, and the construction of normalising transformations, as well as the standard theory derived from the work of R.A. Fisher, H. Cramér, L. Le Cam, and others. The book then examines the close connection between saddle-point approximation and the Laplace method. The final chapter explores series convergence and the acceleration of that convergence.

Stochastic Geometry Spatial Statistics And Random Fields

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Author: Evgeny Spodarev
Publisher: Springer
ISBN: 3642333052
Size: 25.43 MB
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Stochastic Geometry Spatial Statistics And Random Fields by Evgeny Spodarev


Original Title: Stochastic Geometry Spatial Statistics And Random Fields

This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Asymptotic Theory Of Statistics And Probability

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Author: Anirban DasGupta
Publisher: Springer Science & Business Media
ISBN: 0387759700
Size: 30.64 MB
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Asymptotic Theory Of Statistics And Probability by Anirban DasGupta


Original Title: Asymptotic Theory Of Statistics And Probability

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.

Asymptotic Theory In Probability And Statistics With Applications

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Author: Tze-Leung Lai
Publisher: Intl Pr of Boston Inc
ISBN:
Size: 80.99 MB
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Asymptotic Theory In Probability And Statistics With Applications by Tze-Leung Lai


Original Title: Asymptotic Theory In Probability And Statistics With Applications

A collection of 18 papers, many of which are surveys, on asymptotic theory in probability and statistics, with applications to a wide variety of problems. This volume comprises three parts: limit theorems, statistics and applications, and mathematical finance and insurance. It is intended for graduate students in probability and statistics, and for researchers in related areas.

Approximation Theorems Of Mathematical Statistics

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Author: Robert J. Serfling
Publisher: John Wiley & Sons
ISBN: 0470317191
Size: 64.52 MB
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Approximation Theorems Of Mathematical Statistics by Robert J. Serfling


Original Title: Approximation Theorems Of Mathematical Statistics

Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures

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