## Book description

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 R covers the traditiona

1. Preliminaries
2. Preface
3. Chapter 1 Introduction
1. 1.1 Computational Statistics and Statistical Computing
2. 1.2 The R Environment
3. 1.3 Getting Started with R
4. 1.4 Using the R Online Help System
5. 1.5 Functions
6. 1.6 Arrays, Data Frames, and Lists
7. 1.7 Workspace and Files
8. 1.8 Using Scripts
9. 1.9 Using Packages
10. 1.10 Graphics
4. Chapter 2 Probability and Statistics Review
1. 2.1 Random Variables and Probability
2. 2.2 Some Discrete Distributions
3. 2.3 Some Continuous Distributions
4. 2.4 Multivariate Normal Distribution
5. 2.5 Limit Theorems
6. 2.6 Statistics
7. 2.7 Bayes’ Theorem and Bayesian Statistics
8. 2.8 Markov Chains
5. Chapter 3 Methods for Generating Random Variables
1. 3.1 Introduction
2. 3.2 The Inverse Transform Method
3. 3.3 The Acceptance-Rejection Method
4. 3.4 Transformation Methods
5. 3.5 Sums and Mixtures
6. 3.6 Multivariate Distributions
1. 3.6.1 Multivariate Normal Distribution
2. 3.6.2 Mixtures of Multivariate Normals
3. 3.6.3 Wishart Distribution
4. 3.6.4 Uniform Distribution on the d-Sphere
7. 3.7 Stochastic Processes
8. Exercises
6. Chapter 4 Visualization of Multivariate Data
1. 4.1 Introduction
2. 4.2 Panel Displays
3. 4.3 Surface Plots and 3D Scatter Plots
1. 4.3.1 Surface plots
2. 4.3.2 Three-dimensional scatterplot
4. 4.4 Contour Plots
5. 4.5 Other 2D Representations of Data
6. 4.6 Other Approaches to Data Visualization
7. Exercises
7. Chapter 5 Monte Carlo Integration and Variance Reduction
1. 5.1 Introduction
2. 5.2 Monte Carlo Integration
1. 5.2.1 Simple Monte Carlo estimator
2. 5.2.2 Variance and Efficiency
3. 5.3 Variance Reduction
4. 5.4 Antithetic Variables
5. 5.5 Control Variates
6. 5.6 Importance Sampling
7. 5.7 Stratified Sampling
8. 5.8 Stratified Importance Sampling
9. Exercises
10. R Code
8. Chapter 6 Monte Carlo Methods in Inference
1. 6.1 Introduction
2. 6.2 Monte Carlo Methods for Estimation
1. 6.2.1 Monte Carlo estimation and standard error
2. 6.2.2 Estimation of MSE
3. 6.2.3 Estimating a confidence level
3. 6.3 Monte Carlo Methods for Hypothesis Tests
1. 6.3.1 Empirical Type I error rate
2. 6.3.2 Power of a Test
3. 6.3.3 Power comparisons
4. 6.4 Application: “Count Five” Test for Equal Variance
5. Exercises
6. Projects
9. Chapter 7 Bootstrap and Jackknife
1. 7.1 The Bootstrap
2. 7.2 The Jackknife
3. 7.3 Jackknife-after-Bootstrap
4. 7.4 Bootstrap Confidence Intervals
5. 7.5 Better Bootstrap Confidence Intervals
6. 7.6 Application: Cross Validation
7. Exercises
8. Projects
10. Chapter 8 Permutation Tests
1. 8.1 Introduction
2. 8.2 Tests for Equal Distributions
3. 8.3 Multivariate Tests for Equal Distributions
4. 8.4 Application: Distance Correlation
5. Exercises
6. Projects
11. Chapter 9 Markov Chain Monte Carlo Methods
1. 9.1 Introduction
2. 9.2 The Metropolis-Hastings Algorithm
3. 9.3 The Gibbs Sampler
4. 9.4 Monitoring Convergence
5. 9.5 Application: Change Point Analysis
6. Exercises
7. R Code
12. Chapter 10 Probability Density Estimation
1. 10.1 Univariate Density Estimation
1. 10.1.1 Histograms
2. 10.1.2 Frequency Polygon Density Estimate
3. 10.1.3 The Averaged Shifted Histogram
2. 10.2 Kernel Density Estimation
3. 10.3 Bivariate and Multivariate Density Estimation
1. 10.3.1 Bivariate Frequency Polygon
2. 10.3.2 Bivariate ASH
3. 10.3.3 Multidimensional kernel methods
4. 10.4 Other Methods of Density Estimation
5. Exercises
6. R Code
13. Chapter 11 Numerical Methods in R
1. 11.1 Introduction
2. 11.2 Root-finding in One Dimension
3. 11.3 Numerical Integration
4. 11.4 Maximum Likelihood Problems
5. 11.5 One-dimensional Optimization
6. 11.6 Two-dimensional Optimization
7. 11.7 The EM Algorithm
8. 11.8 Linear Programming – The Simplex Method
9. 11.9 Application: Game Theory
10. Exercises
14. Appendix A Notation
15. Appendix B Working with Data Frames and Arrays
1. B.1 Resampling and Data Partitioning
2. B.2 Subsetting and Reshaping Data
3. B.3 Data Entry and Data Analysis
1. B.3.1 Manual Data Entry
2. B.3.2 Recoding Missing Values
3. B.3.3 Reading and Converting Dates
4. B.3.4 Importing/exporting .csv files
5. B.3.5 Examples of data entry and analysis
16. References

## Product information

• Title: Statistical Computing with R
• Author(s): Maria L. Rizzo
• Release date: November 2007
• Publisher(s): Chapman and Hall/CRC
• ISBN: 9781498786591