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Asymptotic Statistics

Asymptotic Statistics Author A. W. van der Vaart
ISBN-10 0521784506
Release 2000-06-19
Pages 443
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A mathematically rigorous, practical introduction presenting standard topics plus research.

From Finite Sample to Asymptotic Methods in Statistics

From Finite Sample to Asymptotic Methods in Statistics Author Pranab K. Sen
ISBN-10 9780521877220
Release 2010
Pages 386
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A broad view of exact statistical inference and the development of asymptotic statistical inference.

A User s Guide to Measure Theoretic Probability

A User s Guide to Measure Theoretic Probability Author David Pollard
ISBN-10 0521002893
Release 2002
Pages 351
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This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

Elements of Distribution Theory

Elements of Distribution Theory Author Thomas A. Severini
ISBN-10 052184472X
Release 2005-08-08
Pages 515
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This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

Fundamentals of Nonparametric Bayesian Inference

Fundamentals of Nonparametric Bayesian Inference Author Subhashis Ghosal
ISBN-10 9781108210126
Release 2017-06-26
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Explosive growth in computing power has made Bayesian methods for infinite-dimensional models - Bayesian nonparametrics - a nearly universal framework for inference, finding practical use in numerous subject areas. Written by leading researchers, this authoritative text draws on theoretical advances of the past twenty years to synthesize all aspects of Bayesian nonparametrics, from prior construction to computation and large sample behavior of posteriors. Because understanding the behavior of posteriors is critical to selecting priors that work, the large sample theory is developed systematically, illustrated by various examples of model and prior combinations. Precise sufficient conditions are given, with complete proofs, that ensure desirable posterior properties and behavior. Each chapter ends with historical notes and numerous exercises to deepen and consolidate the reader's understanding, making the book valuable for both graduate students and researchers in statistics and machine learning, as well as in application areas such as econometrics and biostatistics.

Asymptotic Theory of Statistics and Probability

Asymptotic Theory of Statistics and Probability Author Anirban DasGupta
ISBN-10 9780387759708
Release 2008-03-07
Pages 722
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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

Asymptotics in Statistics Author Lucien Le Cam
ISBN-10 9781461211662
Release 2012-12-06
Pages 287
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This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.

Applied Asymptotics

Applied Asymptotics Author A. R. Brazzale
ISBN-10 0521847036
Release 2007-05-31
Pages 236
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First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.

Asymptotic Methods in Statistical Decision Theory

Asymptotic Methods in Statistical Decision Theory Author Lucien Le Cam
ISBN-10 9781461249467
Release 2012-12-06
Pages 742
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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.

Mathematical Statistics

Mathematical Statistics Author Aleksandr Petrovich Korostelev
ISBN-10 9780821852835
Release 2011
Pages 246
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This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises. Prerequisites for the book include senior undergraduate/beginning graduate-level courses in probability and statistics.

Convergence of Stochastic Processes

Convergence of Stochastic Processes Author David Pollard
ISBN-10 9780387909905
Release 1984
Pages 215
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Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.

Approximation Theorems of Mathematical Statistics

Approximation Theorems of Mathematical Statistics Author R. J. Serfling
ISBN-10 0471024031
Release 1980-12-08
Pages 371
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This paperback reprint of one of the best in the field 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.

Analysis of Multivariate and High Dimensional Data

Analysis of Multivariate and High Dimensional Data Author Inge Koch
ISBN-10 9780521887939
Release 2013-12-02
Pages 526
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This modern approach integrates classical and contemporary methods, fusing theory and practice and bridging the gap to statistical learning.

Introduction to Empirical Processes and Semiparametric Inference

Introduction to Empirical Processes and Semiparametric Inference Author Michael R. Kosorok
ISBN-10 0387749780
Release 2007-12-29
Pages 483
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Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.

Bayesian Nonparametrics

Bayesian Nonparametrics Author J.K. Ghosh
ISBN-10 9780387226545
Release 2006-05-11
Pages 308
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This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.

Predictive Statistics

Predictive Statistics Author Bertrand S. Clarke
ISBN-10 9781107028289
Release 2018-04-30
Pages 652
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A bold retooling of statistics to focus directly on predictive performance with traditional and contemporary data types and methodologies.

Empirical Processes in M Estimation

Empirical Processes in M Estimation Author Sara A. Geer
ISBN-10 052165002X
Release 2000-01-28
Pages 286
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Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction.