This book provides an introduction to statistical computing and a critical, balanced presentation of the algorithms and computational methods used in software systems, discussing techniques for implementing algorithms in a computer. It is intended for graduate students in statistics.
Table of Contents
"Introduction Orientation Purpose, Prerequisites Presentation of Algorithms Computer Organization Introduction Components of the Digital Computer System Representation of Numeric Values Floating and Fixed-Point Arithmetic Operations Error in Floating-Point Computation Introduction Types of Error Error Due to Approximation Imposed by the Compute Analyzing Error in a Finite Process Rounding Error in Floating-Point Operations Rounding Error in Two Common Floating-Point Calculations Condition and Numerical Stability Other Methods of Assessing Error in Computations Summary Programming and Statistical Software Programming Languages: Introduction Components of Programming Languages Program Development Statistical Software Approximating Probabilities and Percentage Points in Selected Probability Distributions Notation and General Considerations General Methods in Approximation The Normal Distribution Student's t Distribution The Beta Distribution F Distribution Chi-Square Distribution Random Numbers: Generation, Tests, and Applications Introduction Generation of Uniform Random Numbers Tests of Random Number Generators General Techniques for Generation of Nonuniform Random Variates Generation of Variates from Specific Distributions Applications Selected Computational Methods in Linear Algebra Introduction Methods Based on Orthogonal Transformations Gaussian Elimination and the Sweep Operator Cholesky Decomposition and Rank-One Update Summary Computational Methods for Multiple Linear Regression Analysis Basic Computational Methods Regression Model Building Multiple Regression Under Linear Restrictions Computational Methods for Classification Models Introduction The Special Case of Balance and Completeness for Fixed-Effects Models The General Problem for Fixed-Effects Models Computing Expected Mean Squares and Estimates of Variance Components Unconstrained Optimization and Nonlinear Regression Preliminaries Methods for Unconstrained Minimization Nonlinear Regression Computational Methods Test Problems Model Fitting Based on Criteria Other Than Least Squares Introduction Minimum Lp Norm Estimators Other Robust Estimators Biased Estimation Robust Nonlinear Regression Exercises Selected Multivariate Methods Introduction Canonical Correlations Principal Components Factor Analysis Multivariate Analysis of Variance "
"The publication of this book, I believe, is a milestone. . .Kennedy and Gentle have done an outstanding job of assembling the best techniques from a great variety of sources, establishing a benchmark for the field of statistical computing. "
---Mathematics of Computation
". . .a very impressive text. . .highly readable and well illustrated with examples. . . .the reader who intends to take a hand in designing his own regression and multivariate packages will find a storehouse of information. "
---Journal of the American Statistical Association
". . .a valuable addition to the literature on statistical computing. "