Statistical computing with R 1

S is a powerful environment for the statistical and graphical analysis of data. It provides the tools to implement many statistical ideas that have been made possible by the widespread availability of workstations having good graphics and computational capabilities. This book is a guide to using S environments to perform statistical analyses and provides both an introduction to the use of S and a course in modern statistical methods. Implementations of S are available commercially in S-PLUS(R) workstations and as the Open Source R for a wide range of computer systems. The aim of this book is to show how to use S as a powerful and graphical data analysis system. Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics. Throughout, the emphasis is on presenting practical problems and full analyses of real data sets. Many of the methods discussed are state of the art approaches to topics such as linear, nonlinear and smooth regression models, tree-based methods, multivariate analysis, pattern recognition, survival analysis, time series and spatial statistics. Throughout modern techniques such as robust methods, non-parametric smoothing and bootstrapping are used where appropriate. This fourth edition is intended for users of S-PLUS 6.0 or R 1.5.0 or later. A substantial change from the third edition is updating for the current versions of S-PLUS and adding coverage of R. The introductory material has been rewritten to emphasis the import, export and manipulation of data. Increased computational power allows even more computer-intensive methods to be used, and methods such as GLMMs, MARS, SOM and support vector machines are considered. Cover Page 1 Half Title Page 2 Chapman & Hall/CRC 3 Published Titles 3 Title Page 4 Copyright Page 5 Contents 6 List of Tables 10 List of Figures 12 Preface 16 Chapter 1: Introduction 18 1.1 Computational Statistics and Statistical Computing 18 1.2 The R Environment 20 1.3 Getting Started with R 21 1.4 Using the R Online Help System 24 1.5 Functions 25 1.6 Arrays,Data Frames, and Lists 26 1.7 Workspace and Files 32 1.8 Using Scripts 34 1.9 Using Packages 35 1.10 Graphics 36 Chapter 2: Probability and Statistics Review 38 2.1 Random Variables and Probability 38 2.2 Some Discrete Distributions 42 2.3 Some Continuous Distributions 46 2.4 Multivariate Normal Distribution 50 2.5 Limit Theorems 52 2.6 Statistics 52 2.7 Bayes’ Theorem and Bayesian Statistics 57 2.8 MarkovChains 59 Chapter 3: Methods for Generating Random Variables 64 3.1 Introduction 64 3.2 The Inverse TransformMethod 66 3.3 The Acceptance-Rejection Method 72 3.4 TransformationMethods 75 3.5 Sums andMixtures 78 3.6 Multivariate Distributions 86 3.7 Stochastic Processes 99 Exercises 111 Chapter 4: Visualization of Multivariate Data 114 4.1 Introduction 114 4.2 PanelDisplays 114 4.3 Surface Plots and 3D Scatter Plots 117 4.4 Contour Plots 123 4.5 Other 2D Representations of Data 127 4.6 Other Approaches to Data Visualization 132 Exercises 133 Chapter 5:Monte Carlo Integration and Variance Reduction 136 5.1 Introduction 136 5.2 Monte Carlo Integration 136 5.3 Variance Reduction 143 5.4 Antithetic Variables 145 5.5 Control Variates 149 5.6 Importance Sampling 156 5.7 Stratified Sampling 161 5.8 Stratified Importance Sampling 164 Exercises 166 R Code 169 Chapter 6: Monte Carlo Methods in Inference 170 6.1 Introduction 170 6.2 Monte CarloMethods for Estimation 171 6.3 Monte Carlo Methods for Hypothesis Tests 179 6.4 Application 191 Exercises 197 Chapter 7: Bootstrap and Jackknife 200 7.1 The Bootstrap 200 7.2 The Jackknife 207 7.3 Jackknife-after-Bootstrap 212 7.4 Bootstrap Confidence Intervals 214 7.5 Better Bootstrap Confidence Intervals 220 7.6 Application 224 Exercises 229 Chapter 8: Permutation Tests 232 8.1 Introduction 232 8.2 Tests for Equal Distributions 236 8.3 Multivariate Tests for Equal Distributions 239 8.4 Application 252 Exercises 259 Chapter 9: Markov Chain Monte Carlo Methods 262 9.1 Introduction 262 9.2 The Metropolis-Hastings Algorithm 264 9.3 The Gibbs Sampler 280 9.4 Monitoring Convergence 283 9.5 Application 288 Exercises 294 R Code 296 Chapter 10: Probability Density Estimation 298 10.1 Univariate Density Estimation 298 10.2 KernelDensity Estimation 313 10.3 Bivariate and Multivariate Density Estimation 322 10.4 Other Methods of Density Estimation 331 Exercises 331 R Code 334 Chapter 11: Numerical Methods in R 336 11.1 Introduction 336 11.2 Root-finding in One Dimension 343 11.3 Numerical Integration 347 11.4 MaximumLikelihood Problems 352 11.5 One-dimensional Optimization 355 11.6 Two-dimensional Optimization 359 11.7 The EM Algorithm 362 11.8 Linear Programming – The Simplex Method 365 11.9 Application 366 Exercises 370 Appendix A Notation 372 Appendix B Working with Data Frames and Arrays 374 B.1 Resampling and Data Partitioning 374 B.2 Subsetting and Reshaping Data 377 B.3 Data Entry and Data Analysis 381 References 392 Back Cover 412

s-plus Is A Powerful Environment For The Statistical And Graphical Analysis Of Data. It Provides The Tools To Implement Many Statistical Ideas Which Have Been Made Possible By The Widespread Availability Of Workstations Having Good Graphics And Computational Capabilities. This Book Is A Guide To Using S-plus To Perform Statistical Analyses And Provides Both An Introduction To The Use Of S-plus And A Course In Modern Statistical Methods. S-plus Is Available For Both Windows And Unix Workstations, And Both Versions Are Covered In Depth.

the Aim Of The Book Is To Show How To Use S-plus As A Powerful And Graphical Data Analysis System. Readers Are Assumed To Have A Basic Grounding In Statistics, And So The Book In Intended For Would-be Users Of S-plus And Both Students And Researchers Using Statistics. Throughout, The Emphasis Is On Presenting Practical Problems And Full Analyses Of Real Data Sets. Many Of The Methods Discussed Are State-of-the-art Approaches To Topics Such As Linear, Nonlinear, And Smooth Regression Models, Tree-based Methods, Multivariate Analysis And Pattern Recognition, Survival Analysis, Time Series And Spatial Statistics. Throughout, Modern Techniques Such As Robust Methods, Non-parametric Smoothing, And Bootstrapping Are Used Where Appropriate.

this Third Edition Is Intended For Users Of S-plus 4.5, 5.0, 2000 Or Later, Although S-plus 3.3/4 Are Also Considered. The Major Change From The Second Edition Is Coverage Of The Current Versions Of S-plus. The Material Has Been Extensively Rewritten Using New Examples And The Latest Computationally Intensive Methods. The Companion Volume On S Programming Will Provide An In-depth Guide For Those Writing Software In The S Language.

the Authors Have Written Several Software Libraries That Enhance S-plus; These And All The Datasets Used Are Available On The Internet In Versions For Windows And Unix. There Are Extensive On-line Complements Covering Advanced Material, User-contributed Extensions, Further Exercises, And New Features Of S-plus As They Are Introduced.

dr. Venables Is Now Statistician With Csrio In Queensland, Having Been At The Department Of Statistics, University Of Adelaide, For Many Years Previously. He Has Given Many Short Courses On S-plus In Australia, Europe, And The Usa. Professor Ripley Holds The Chair Of Applied Statistics At The University Of Oxford, And Is The Author Of Four Other Books On Spatial Statistics, Simulation, Pattern Recognition, And Neural Networks.