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Numerical Methods of Statistics / Edition 2

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Overview

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. The book concludes with an examination of sorting, FFT and the application of other "fast" algorithms to statistics. Each chapter contains exercises that range in difficulty as well as examples of the methods at work. Most of the examples are accompanied by demonstration code available on a floppy disk included with the book.
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Editorial Reviews

From the Publisher
Review from the previous edition '… an excellent tool both for self-study and for classroom teaching. It summarizes the state of the art well and provides a solid basis, through the programs that go with the book, for numerical experimentation and further development. All in all, this is a good book to have … I recommend it.' D. Denteneer, Mathematics of Computing

Review from the previous edition: '… this book grew out of notes for a statistical computing course … The goal of this course was to prepare the doctoral students with the computing tools needed for statistical research. I very much liked this book and recommend it for this use.' Jaromir Antoch, Zentralblatt für Mathematik

Review from the previous edition: '… a really nice introduction to numerical analysis. All the classical subjects of a numerical analysis course are discussed in a surprisingly short and clear way … When adapting the examples, the first half of the book can be used as a numerical analysis course for any other discipline …' Adhemar Bultheel, Bulletin of the Belgian Mathematical Society

Review from the previous edition: '… an extremely readable book. This would be an excellent book for a graduate-level course in statistical computing.' Journal of the American Statistical Association

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Product Details

Meet the Author

John F. Monahan is a Professor of Statistics at North Carolina State University where he joined the faculty in 1978 and has been a professor since 1990. His research has appeared in numerous computational as well as statistical journals. He is also the author of A Primer on Linear Models (2008).
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Table of Contents

Preface
1 Algorithms and Computers 1
2 Computer Arithmetic 11
3 Matrices and Linear Equations 37
4 More Methods for Solving Linear Equations 61
5 Regression Computations 82
6 Eigenproblems 114
7 Functions: Interpolation, Smoothing, and Approximation 137
8 Introduction to Optimization and Nonlinear Equations 170
9 Maximum Likelihood and Nonlinear Regression 199
10 Numerical Integration and Monte Carlo Methods 235
11 Generating Random Variables from other Distributions 279
12 Statistical Methods for Integration and Monte Carlo 319
13 Markov Chain Monte Carlo Methods 351
14 Sorting and Fast Algorithms 379
Table of Programs and Demonstrations 415
Author Index 419
Subject Index 425
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