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Mathematics - Probability Theory and Stochastic Processes | Computational Statistics

Computational Statistics

2009, XXII, 728 p.

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  • Provides comprehensive coverage of modern computationally intensive statistical methods
  • Covers the topics in numerical analysis necessary for accurate and efficient implementation of the methods of computational statistics
  • Emphasizes the unity of the methods of computational inference

Computational inference has taken its place alongside asymptotic inference and exact techniques in the standard collection of statistical methods. Computational inference is based on an approach to statistical methods that uses modern computational power to simulate distributional properties of estimators and test statistics. This book describes computationally-intensive statistical methods in a unified presentation, emphasizing techniques, such as the PDF decomposition, that arise in a wide range of methods.

The book assumes an intermediate background in mathematics, computing, and applied and theoretical statistics. The first part of the book, consisting of a single long chapter, reviews this background material while introducing computationally-intensive exploratory data analysis and computational inference.

The six chapters in the second part of the book are on statistical computing. This part describes arithmetic in digital computers and how the nature of digital computations affects algorithms used in statistical methods. Building on the first chapters on numerical computations and algorithm design, the following chapters cover the main areas of statistical numerical analysis, that is, approximation of functions, numerical quadrature, numerical linear algebra, solution of nonlinear equations, optimization, and random number generation.

The third and fourth parts of the book cover methods of computational statistics, including Monte Carlo methods, randomization and cross validation, the bootstrap, probability density estimation, and statistical learning.

The book includes a large number of exercises with some solutions provided in an appendix.

James E. Gentle is University Professor of Computational Statistics at George Mason University. He is a Fellow of the American Statistical Association (ASA) and of the American Association for the Advancement of Science. He has held several national offices in the ASA and has served as associate editor of journals of the ASA as well as for other journals in statistics and computing. He is author of Random Number Generation and Monte Carlo Methods and Matrix Algebra.

Content Level » Research

Keywords » Estimator - Monte Carlo method - Partition - STATISTICA - bootstrap - clustering and classification - data analysis - linear algebra - nonparametric probability density estimation - numerical methods - random number generation

Related subjects » Computational Science & Engineering - Computational Statistics - Database Management & Information Retrieval - Probability Theory and Stochastic Processes - Theoretical Computer Science

Table of contents 

Preliminaries.- Mathematical and Statistical Preliminaries.- Statistical Computing.- Computer Storage and Arithmetic.- Algorithms and Programming.- Approximation of Functions and Numerical Quadrature.- Numerical Linear Algebra.- Solution of Nonlinear Equations and Optimization.- Generation of Random Numbers.- Methods of Computational Statistics.- Graphical Methods in Computational Statistics.- Tools for Identification of Structure in Data.- Estimation of Functions.- Monte Carlo Methods for Statistical Inference.- Data Randomization, Partitioning, and Augmentation.- Bootstrap Methods.- Exploring Data Density and Relationships.- Estimation of Probability Density Functions Using Parametric Models.- Nonparametric Estimation of Probability Density Functions.- Statistical Learning and Data Mining.- Statistical Models of Dependencies.

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