Statistical Computing With R

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2007-11-15
  • Publisher: Chapman & Hall/

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Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with Rcovers the traditional core material of computational statistics, with an emphasis on using the R language via an examples-based approach. Suitable for an introductory course in computational statistics or for self-study, it includes R code for all examples and R notes to help explain the R programming concepts. After an overview of computational statistics and an introduction to the R computing environment, the book reviews some basic concepts in probability and classical statistical inference. Each subsequent chapter explores a specific topic in computational statistics. These chapters cover the simulation of random variables from probability distributions, thevisualization of multivariate data, Monte Carlo integration and variance reduction methods, Monte Carlo methods in inference, bootstrap and jackknife, permutation tests, Markov chain Monte Carlo (MCMC) methods, and density estimation. The final chapter presents a selection of examples that illustrate the application of numerical methods using R functions. Focusing on implementation rather than theory, this text serves as a balanced, accessible introduction to computational statistics and statistical computing.

Author Biography

Maria L. Rizzo Bowling Green State University, Bowling Green, Ohio, U.S.A.

Table of Contents

Prefacep. xv
Introductionp. 1
Computational Statistics and Statistical Computingp. 1
The R Environmentp. 3
Getting Started with Rp. 4
Using the R Online Help Systemp. 7
Functionsp. 8
Arrays, Data Frames, and Listsp. 9
Workspace and Filesp. 15
Using Scriptsp. 17
Using Packagesp. 18
Graphicsp. 19
Probability and Statistics Reviewp. 21
Random Variables and Probabilityp. 21
Some Discrete Distributionsp. 25
Some Continuous Distributionsp. 29
Multivariate Normal Distributionp. 33
Limit Theoremsp. 35
Statisticsp. 35
Bayes' Theorem and Bayesian Statisticsp. 40
Markov Chainsp. 42
Methods for Generating Random Variablesp. 47
Introductionp. 47
The Inverse Transform Methodp. 49
The Acceptance-Rejection Methodp. 55
Transformation Methodsp. 58
Sums and Mixturesp. 61
Multivariate Distributionsp. 69
Stochastic Processesp. 82
Exercisesp. 94
Visualization of Multivariate Datap. 97
Introductionp. 97
Panel Displaysp. 97
Surface Plots and 3D Scatter Plotsp. 100
Contour Plotsp. 106
Other 2D Representations of Datap. 110
Other Approaches to Data Visualizationp. 115
Exercisesp. 116
Monte Carlo Integration and Variance Reductionp. 119
Introductionp. 119
Monte Carlo Integrationp. 119
Variance Reductionp. 126
Antithetic Variablesp. 128
Control Variatesp. 132
Importance Samplingp. 139
Stratified Samplingp. 144
Stratified Importance Samplingp. 147
Exercisesp. 149
R Codep. 152
Monte Carlo Methods in Inferencep. 153
Introductionp. 153
Monte Carlo Methods for Estimationp. 154
Monte Carlo Methods for Hypothesis Testsp. 162
Applicationp. 174
Exercisesp. 180
Bootstrap and Jackknifep. 183
The Bootstrapp. 183
The Jackknifep. 190
Jackknife-after-Bootstrapp. 195
Bootstrap Confidence Intervalsp. 197
Better Bootstrap Confidence Intervalsp. 203
Applicationp. 207
Exercisesp. 212
Permutation Testsp. 215
Introductionp. 215
Tests for Equal Distributionsp. 219
Multivariate Tests for Equal Distributionsp. 222
Applicationp. 235
Exercisesp. 242
Markov Chain Monte Carlo Methodsp. 245
Introductionp. 245
The Metropolis-Hastings Algorithmp. 247
The Gibbs Samplerp. 263
Monitoring Convergencep. 266
Applicationp. 271
Exercisesp. 277
R Codep. 279
Probability Density Estimationp. 281
Univariate Density Estimationp. 281
Kernel Density Estimationp. 296
Bivariate and Multivariate Density Estimationp. 305
Other Methods of Density Estimationp. 314
Exercisesp. 314
R Codep. 317
Numerical Methods in Rp. 319
Introductionp. 319
Root-finding in One Dimensionp. 326
Numerical Integrationp. 330
Maximum Likelihood Problemsp. 335
One-dimensional Optimizationp. 338
Two-dimensional Optimizationp. 342
The EM Algorithmp. 345
Linear Programming - The Simplex Methodp. 348
Applicationp. 349
Exercisesp. 353
Notationp. 355
Working with Data Frames and Arraysp. 357
Resampling and Data Partitioningp. 357
Subsetting and Reshaping Datap. 360
Data Entry and Data Analysisp. 364
Referencesp. 375
Indexp. 395
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