Contents Preface v 1 Methods of Computational Statistics 1 Introduction to Part 1 3 1 Preliminaries 5 1.1 Discovering Structure: Data Structures and Structure in Data 6 1.2 Modeling and Computational Inference 8 1.3 The Role of the Empirical Cumulative Distribution Function 11 1.4 The Role of Optimization in Inference 15 1.5 Inference about Functions 30 1.6 Probability Statements in Statistical Inference 32 Exercises 35 2 Monte Carlo Methods for Statistical Inference 39 2.1 Generation of Random Numbers 40 2.2 Monte Carlo Estimation 53 2.3 Simulation of Data from a Hypothesized Model: Monte Carlo Tests 58 2.4 Simulation of Data from a Fitted Model:"Parametric Bootstraps" 60 2.5 Random Sampling from Data 60 2.6 Reducing Variance in Monte Carlo Methods 61 2.7 Acceleration of Markov Chain Monte Carlo Methods 65 Exercises 66 3 Randomization and Data Partitioning 69 3.1 Randomization Methods 70 3.2 Cross Validation for Smoothing and Fitting 74 3.3 Jackknife Methods 76 Further Reading 82 Exercises 83 4 Bootstrap Methods 85 4.1 Bootstrap Bias Corrections 86 4.2 Bootstrap Estimation of Variance 88 4.3 Bootstrap Confidence Intervals 89 4.4 Bootstrapping Data with Dependencies 93 4.5 Variance Reduction in Monte Carlo Bootstrap 94 Further Reading 96 Exercises 97 5 Tools for Identification of Structure in Data 99 5.1 Linear Structure and Other Geometric Properties 100 5.2 Linear Transformations 101 5.3 General Transformations of the Coordinate System 108 5.4 Measures of Similarity and Dissimilarity 109 5.5 Data Mining 123 5.6 Computational Feasibility 124 Exercises 125 6 Estimation of Functions 127 6.1 General Methods for Estimating Functions 128 6.2 Pointwise Properties of Function Estimators 143 6.3 Global Properties of Estimators of Functions 146 Exercises 150 7 Graphical Methods in Computational Statistics 153 7.1 Viewing One, Two, or Three Variables 155 7.2 Viewing Multivariate Data 168 7.3 Hardware and Low-Level Software for Graphics 184 7.4 Software for Graphics Applications 186 Further Reading 188 Exercises 188 II Exploring Data Density and Structure 191 Introduction to Part 11 193 8 Estimation of Probability Density Functions Using Parametric Models 197 8.1 Fitting a Parametric Probability Distribution 198 8.2 General Families of Probability Distributions 199 8.3 Mixtures of Parametric Families 202 Exercises 203 9 Nonparametric Estimation of Probability Density Functions 205 9.1 The Likelihood Function 206 9.2 Histogram Estimators 208 9.3 Kernel Estimators 217 9.4 Choice of Window Widths 222 9.5 Orthogonal Series Estimators 222 9.6 Other Methods of Density Estimation 224 Exercises 226 10 Structure in Data 233 10.1 Clustering and Classification 237 10.2 Ordering and Ranking Multivariate Data 255 10.3 Linear Principal Components 264 10 .4 Variants of Principal Components 276 10.5 Projection Pursuit 281 10.6 Other Methods for Identifying Structure 289 10.7 Higher Dimensions 290 Exercises 294 11 Statistical Models of Dependencies 299 11. 1 Regression and Classificat ion Models 301 11.2 Probability Distributions in Models 308 11.3 Fitting Models to Data 311 Exercises 333 Appendices 336 A Monte Carlo Studies in Statistics 337 A.1 Simulation as an Experiment 338 A.2 Reporting Simulation Experiments 339 A.3 An Example 340 A.4 Computer Experiments 347 Exercises 349 B Software for Random Number Generation 351 B.1 The User Interface for Random Number Gencrators 353 B.2 Controlling the Seeds in Monte Carlo Studies 354 B.3 Random Number Generation in IMSL Libraries 354 B.4 Random Number Generat ion in S-Plus and R 357 C Notation and Definitions 363 D Solutions and Hints for Selected Exercises 377 Bibliography 385 Literature in Computational Statistics 386 Resources A vailable over the Internet 387 References for Software Packages 389 References to the Literature 389 Author Index 409 Subject Index 415