Asymptotic Statistics

Author: A. W. van der Vaart
Publisher: Cambridge University Press
ISBN: 9780521784504
Format: PDF, ePub, Mobi
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A mathematically rigorous, practical introduction presenting standard topics plus research.

Numerical Methods of Statistics

Author: John F. Monahan
Publisher: Cambridge University Press
ISBN: 1139498002
Format: PDF, ePub, Mobi
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This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.

Applied Asymptotics

Author: A. R. Brazzale
Publisher: Cambridge University Press
ISBN: 9780521847032
Format: PDF, Docs
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First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.

Brownian Motion

Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Format: PDF, ePub, Docs
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This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Predictive Statistics

Author: Bertrand S. Clarke
Publisher: Cambridge University Press
ISBN: 110863303X
Format: PDF, ePub, Mobi
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All scientific disciplines prize predictive success. Conventional statistical analyses, however, treat prediction as secondary, instead focusing on modeling and hence estimation, testing, and detailed physical interpretation, tackling these tasks before the predictive adequacy of a model is established. This book outlines a fully predictive approach to statistical problems based on studying predictors; the approach does not require predictors correspond to a model although this important special case is included in the general approach. Throughout, the point is to examine predictive performance before considering conventional inference. These ideas are traced through five traditional subfields of statistics, helping readers to refocus and adopt a directly predictive outlook. The book also considers prediction via contemporary 'black box' techniques and emerging data types and methodologies where conventional modeling is so difficult that good prediction is the main criterion available for evaluating the performance of a statistical method. Well-documented open-source R code in a Github repository allows readers to replicate examples and apply techniques to other investigations.

The Jackknife and Bootstrap

Author: Jun Shao
Publisher: Springer Science & Business Media
ISBN: 1461207959
Format: PDF, ePub
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The jackknife and bootstrap are the most popular data-resampling meth ods used in statistical analysis. The resampling methods replace theoreti cal derivations required in applying traditional methods (such as substitu tion and linearization) in statistical analysis by repeatedly resampling the original data and making inferences from the resamples. Because of the availability of inexpensive and fast computing, these computer-intensive methods have caught on very rapidly in recent years and are particularly appreciated by applied statisticians. The primary aims of this book are (1) to provide a systematic introduction to the theory of the jackknife, the bootstrap, and other resampling methods developed in the last twenty years; (2) to provide a guide for applied statisticians: practitioners often use (or misuse) the resampling methods in situations where no theoretical confirmation has been made; and (3) to stimulate the use of the jackknife and bootstrap and further devel opments of the resampling methods. The theoretical properties of the jackknife and bootstrap methods are studied in this book in an asymptotic framework. Theorems are illustrated by examples. Finite sample properties of the jackknife and bootstrap are mostly investigated by examples and/or empirical simulation studies. In addition to the theory for the jackknife and bootstrap methods in problems with independent and identically distributed (Li.d.) data, we try to cover, as much as we can, the applications of the jackknife and bootstrap in various complicated non-Li.d. data problems.

The Review of Economic Studies

Format: PDF, Kindle
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The object of the Review of Economic Studies is to encourage research in theoretical and applied economics, especially by young economists, and to publish the results in the Review.

Convergence of Stochastic Processes

Author: David Pollard
Publisher: David Pollard
ISBN: 0387909907
Format: PDF, Mobi
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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.