Computational Statistics: An Introduction to R

Suitable for a compact course or self-study, Computational Statistics: An Introduction to Rillustrates how to use the freely available R software package for data analysis, statistical programming, and graphics. Integrating R code and examples throughout, the text only requires basic knowledge of statistics and computing.This introduction covers one-sample analysis and distribution diagnostics, regression, two-sample problems and comparison of distributions, and multivariate analysis. It uses a range of examples to demonstrate how R can be employed to tackle statistical problems. In addition, the handy appendix includes a collection of R language elements and functions, serving as a quick reference and starting point to access the rich information that comes bundled with R.Accessible to a broad audience, this book explores key topics in data analysis, regression, statistical distributions, and multivariate statistics. Full of examples and with a color insert, it helps readersbecome familiar with R.

Introduction	p. v
Basic Data Analysis	p. 1
R Programming Conventions	p. 1
Generation of Random Numbers and Patterns	p. 4
Random Numbers	p. 4
Patterns	p. 9
Case Study: Distribution Diagnostics	p. 10
Distribution Functions	p. 13
Histograms	p. 17
Barcharts	p. 21
Statistics of Distribution Functions: Kolmogorov-Smirnov Tests	p. 22
Monte Carlo Confidence Bands	p. 23
Statistics of Histograms and Related Plots; X2-Tests	p. 29
Moments and Quantiles	p. 34
R Complements	p. 39
Random Numbers	p. 39
Graphical Comparisons	p. 40
Functions	p. 46
Enhancing Graphical Displays	p. 50
R Internals	p. 53
parse	p. 53
eval	p. 53
print	p. 54
Executing Files	p. 54
Packages	p. 54
Statistical Summary	p. 56
Literature and Additional References	p. 57
Regression	p. 59
General Regression Model	p. 59
Linear Model	p. 60
Factors	p. 63
Least Squares Estimation	p. 64
Regression Diagnostics	p. 69
More Examples for Linear Models	p. 75
Model Formulae	p. 76
Gauss-Markov Estimator and Residuals	p. 77
Variance Decomposition and Analysis of Variance	p. 79
Simultaneous Inference	p. 85
Scheffé's Confidence Bands	p. 85
Tukey's Confidence Intervals	p. 87
Case Study: Titre Plates	p. 88
Beyond Linear Regression	p. 96
Transformations	p. 96
Generalised Linear Models	p. 96
Local Regression	p. 97
R Complements	p. 101
Discretisation	p. 101
External Data	p. 101
Testing Software	p. 101
R Data Types	p. 102
Classes and Polymorphic Functions	p. 103
Extractor Functions	p. 104
Statistical Summary	p. 105
Literature and Additional References	p. 105
Comparisons	p. 107
Shift/Scale Families, and Stochastic Order	p. 109
QQ Plot, PP Plot, and Comparison of Distributions	p. 111
Kolmogorov-Smirnov Tests	p. 116
Tests for Shift Alternatives	p. 117
A Road Map	p. 125
Power and Confidence	p. 126
Theoretical Power and Confidence	p. 126
Simulated Power and Confidence	p. 130
Quantile Estimation	p. 133
Qualitative Features of Distributions	p. 135
Statistical Summary	p. 136
Literature and Additional References	p. 137
Dimensions 1, 2, 3, ..., ¿	p. 139
R Complements	p. 140
Dimensions	p. 143
Selections	p. 145
Projections	p. 145
Marginal Distributions and Scatter Plot Matrices	p. 145
Projection Pursuit	p. 150
Projections for Dimensions 1, 2, 3, ...7	p. 153
Parallel Coordinates	p. 154
Sections, Conditional Distributions and Coplots	p. 156
Transformation and Dimension Reduction	p. 162
Higher Dimensions	p. 167
Linear Case	p. 167
Partial Residuals and Added Variable Plots	p. 168
Non-Linear Case	p. 169
Example: Cusp Non-Linearity	p. 169
Case Study: Melbourne Temperature Data	p. 173
Curse of Dimensionality	p. 174
Case Study: Body Fat	p. 175
High Dimensions	p. 189
Statistical Summary	p. 190
R as a Programming Language and Environment	p. 193
Help and Information	p. 193
Names and Search Paths	p. 195
Administration and Customisation	p. 196
Basic Data Types	p. 197
Output for Objects	p. 199
Object Inspection	p. 200
System Inspection	p. 201
Complex Data Types	p. 202
Accessing Components	p. 204
Data Manipulation	p. 206
Operators	p. 208
Functions	p. 209
Debugging and Profiling	p. 211
Control Structures	p. 213
Input and Output to Data Streams; External Data	p. 215
Libraries, Packages	p. 218
Mathematical Operators and Functions; Linear Algebra	p. 220
Model Descriptions	p. 221
Graphic Functions	p. 223
High-Level Graphics	p. 223
Low-Level Graphics	p. 224
Annotations and Legends	p. 225
Graphic Parameters and Layout	p. 226
Elementary Statistical Functions	p. 227
Distributions, Random Numbers, Densities...	p. 228
Computing on the Language	p. 231
References	p. 233
Functions and Variables by Topic	p. 237
Function and Variable Index	p. 245
Subject Index	p. 249
Table of Contents provided by Ingram. All Rights Reserved.

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Computational Statistics: An Introduction to R

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