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Numerical methods of statistics. (English) Zbl 0969.65007

Cambridge Series in Statistical and Probabilistic Mathematics. 7. Cambridge: Cambridge University Press. xiv, 428 p. (2001).
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 provides a basic background in numerical analysis, emphasizing issues that are 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 an unified manner that reflects complementary views of Monte Carlo methods. The book concludes with an examination of sorting, the fast Fourier transform, and the application of other “fast” algorithms to statistics.
Each chapter contains exercises that range from the simple to research problems, 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.
As the author says in the preface, this book grew out of notes for his Statistical Computing Course he has been teaching for the past 20 years. The goal of this course was to prepare the doctoral students with the computing tools needed for statistical research. I liked very much this book and must recommend it for this type of the use.
Contents: 1. Algorithms and computers; 2. Computer arithmetic; 3. Matrices and linear equations; 4. More methods for solving linear equations; 5. Regression computation; 6. Eigenproblems; 7. Functions: Interpolation, smoothing and approximation; 8 Introduction to optimization and nonlinear equations; 9. Maximum likelihood and nonlinear regression; 10. Numerical integration and Monte Carlo; 11. Generating random variables from other distributions; 12. Statistical methods for integration and Monte Carlo; 13. Monte Carlo Markov chains 14. Sorting and fast algorithms.

MSC:

65C60 Computational problems in statistics (MSC2010)
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62J02 General nonlinear regression
65C10 Random number generation in numerical analysis
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
68P10 Searching and sorting
65Fxx Numerical linear algebra
65T50 Numerical methods for discrete and fast Fourier transforms
65D32 Numerical quadrature and cubature formulas
65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods

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