Numerical Methods Of Statistics

This page intentionally left blank Numerical Methods of Statistics Second Edition 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 on the author’s Web site. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder-Mead search algorithm. 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). CAMBRIDGE SERIES IN STATISTICAL AND PROBABILISTIC MATHEMATICS Editorial Board Z. Ghahramani, Department of Engineering, University of Cambridge R. Gill, Department of Mathematics, Utrecht University F. Kelly, Statistics Laboratory, University of Cambridge B. D. Ripley, Department of Statistics, University of Oxford S. Ross, Epstein Department of Industrial & Systems Engineering, University of Southern California M. Stein, Department of Statistics, University of Chicago This series of high-quality upper-division textbooks and expository monographs covers all aspects of stochastic applicable mathematics. The topics range from pure and applied statistics to probability theory, operations research, optimization, and mathematical programming. The books contain clear presentations of new developments in the field and also of the state of the art in classical methods. While emphasizing rigorous treatment of theoretical methods, the books also contain applications and discussions of new techniques made possible by advances in computational practice. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. Bootstrap Methods and Their Application, by A. C. Davison and D. V. Hinkley Markov Chains, by J. Norris Asymptotic Statistics, by A. W. van der Vaart Wavelet Methods for Time Series Analysis, by Donald B. Percival and Andrew T. Walden Bayesian Methods, by Thomas Leonard and John S. J. Hsu Empirical Processes in M-Estimation, by Sara van de Geer Numerical Methods of Statistics, by John F. Monahan A User’s Guide to Measure Theoretic Probability, by David Pollard The Estimation and Tracking of Frequency, by B. G. Quinn and E. J. Hannan Data Analysis and Graphics Using R, by John Maindonald and John Braun Statistical Models, by A. C. Davison Semiparametric Regression, by D. Ruppert, M. P. Wand, and R. J. Carroll Exercise in Probability, by Loic Chaumont and Marc Yor Statistical Analysis of Stochastic Processes in Time, by J. K. Lindsey Measure Theory and Filtering, by Lakhdar Aggoun and Robert Elliott Essentials of Statistical Inference, by G. A. Young and R. L. Smith Elements of Distribution Theory, by Thomas A. Severini Statistical Mechanics of Disordered Systems, by Anton Bovier The Coordinate-Free Approach to Linear Models, by Michael J. Wichura Random Graph Dynamics, by Rick Durrett Networks, b