Elements of Computational Statistics

Computationally intensive methods have become widely used both for statistical inference and for exploratory analyses of data. The methods of computational statistics involve resampling, partitioning, and multiple transformations of a dataset. They may also make use of randomly generated artificial data. Implementation of these methods often requires advanced techniques in numerical analysis, so there is a close connection between computational statistics and statistical computing. This book describes techniques used in computational statistics, and addresses some areas of application of computationally intensive methods, such as density estimation, identification of structure in data, and model building. Although methods of statistical computing are not emphasized in this book, numerical techniques for transformations, for function approximation, and for optimization are explained in the context of the statistical methods. The book includes exercises, some with solutions. The book can be used as a text or supplementary text for various courses in modern statistics at the advanced undergraduate or graduate level, and it can also be used as a reference for statisticians who use computationally-intensive methods of analysis. Although some familiarity with probability and statistics is assumed, the book reviews basic methods of inference, and so is largely self-contained. James Gentle is University Professor of Computational Statistics at George Mason University. He is a Fellow of the American Statistical Association and a member of the International Statistical Institute. He has held several national offices in the American Statistical Association and has served as associate editor for journals of the ASA as well as for other journals in statistics and computing. He is the author of Random Number Generation and Monte Carlo Methods and Numerical Linear Algebra for Statistical Applications.