Numerical Methods of Statistics

Author: John F. Monahan
Publisher: Cambridge University Press
ISBN: 1139498002
Format: PDF, 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.

Brownian Motion

Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Format: PDF, Kindle
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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.

Asymptotic Statistics

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

Applied Asymptotics

Author: A. R. Brazzale
Publisher: Cambridge University Press
ISBN: 1139463837
Format: PDF, ePub, Docs
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In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.

Empirical Processes in M Estimation

Author: Sara A. van de Geer
Publisher: Cambridge University Press
ISBN: 9780521650021
Format: PDF
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Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction.

Asymptotics in Statistics

Author: Lucien Le Cam
Publisher: Springer Science & Business Media
ISBN: 9780387950365
Format: PDF
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Most of the subsequent chapters have been entirely rewritten, and the nonparametrics of Chapter 7 have been amplified.".