Test Banks For Statistical Computing with R 2nd Edition by Maria L. Rizzo, 9781466553323, Chapter 1-15 Complete Guide

Statistical Computing with R 2nd Edition 3323 7760 4, 2, 2, 3323, 3330, 2760 1 Introduction 1.1 Statistical Computing 1.2 The R Environment 1.3 Getting Started with R and RStudio 1.4 Basic Syntax 1.5 Using the R Online Help System 1.6 Distributions and Statistical Tests 1.7 Functions 1.8 Arrays, Data Frames, and Lists 1.9 Formula Specification 1.10 Graphics 1.11 Introduction to ggplot 1.12 Workspace and Files 1.12.1 The Working Directory 1.12.2 Reading Data from External Files 1.12.3 Importing/Exporting .csv Files 1.13 Using Scripts 1.14 Using Packages 1.15 Using R Markdown and knitr 2 Probability and Statistics Review 2.1 Random Variables and Probability 2.2 Some Discrete Distributions 2.3 Some Continuous Distributions 2.4 Multivariate Normal Distribution 2.5 Limit Theorems 2.6 Statistics 2.7 Bayes’ Theorem and Bayesian Statistics 2.8 Markov Chains 3 Methods for Generating Random Variables 3.1 Introduction 3.2 The Inverse Transform Method 3.2.1 Inverse Transform Method, Continuous Case 3.2.2 Inverse Transform Method, Discrete Case 3.3 The Acceptance-Rejection Method 3.4 Transformation Methods 3.5 Sums and Mixtures 3.6 Multivariate Distributions 3.6.1 Multivariate Normal Distribution 3.6.2 Mixtures of Multivariate Normals 3.6.3 Wishart Distribution 3.6.4 Uniform Distribution on the d-Sphere 4 Generating Random Processes 4.1 Stochastic Processes 4.1.1 Poisson Processes 4.1.2 Renewal Processes 4.1.3 Symmetric Random Walk 4.2 Brownian Motion 5 Visualization of Multivariate Data 5.1 Introduction 5.2 Panel Displays 5.3 Correlation Plots 5.4 Surface Plots and 3D Scatter Plots 5.4.1 Surface Plots 5.4.2 Three-dimensional Scatterplot 5.5 Contour Plots 5.6 Other 2D Representations of Data 5.6.1 Andrews Curves 5.6.2 Parallel Coordinate Plots 5.6.3 Segments, Stars, and Other Representations 5.7 Principal Components Analysis 5.8 Other Approaches to Data Visualization 5.9 Additional Resources 6 Monte Carlo Integration and Variance Reduction 6.1 Introduction 6.2 Monte Carlo Integration 6.2.1 Simple Monte Carlo Estimator 6.2.2 Variance and Efficiency 6.3 Variance Reduction 6.4 Antithetic Variables 6.5 Control Variates 6.5.1 Antithetic Variate as Control Variate 6.5.2 Several Control Variates 6.5.3 Control Variates and Regression 6.6 Importance Sampling 6.7 Stratified Sampling 6.8 Stratified Importance Sampling 7 Monte Carlo Methods in Inference 7.1 Introduction 7.2 Monte Carlo Methods for Estimation 7.2.1 Monte Carlo Estimation and Standard Error 7.2.2 Estimation of MSE 7.2.3 Estimating a Confidence Level 7.3 Monte Carlo Methods for Hypothesis Tests 7.3.1 Empirical Type I Error Rate 7.3.2 Power of a Test 7.3.3 Power Comparisons 7.4 Application: “Count Five” Test for Equal Variance 8 Bootstrap and Jackknife 8.1 The Bootstrap 8.1.1 Bootstrap Estimation of Standard Error 8.1.2 Bootstrap Estimation of Bias 8.2 The Jackknife 8.3 Bootstrap Confidence Intervals 8.3.1 The Standard Normal Bootstrap Confidence Interval 8.3.2 The Basic Bootstrap Confidence Interval 8.3.3 The Percentile Bootstrap Confidence Interval 8.3.4 The Bootstrap t Interval 8.4 Better Bootstrap Confidence Intervals 8.5 Application: Cross Validation 9 Resampling Applications 9.1 Jackknife-after-Bootstrap 9.2 Resampling for Regression Models 9.2.1 Resampling Cases 9.2.2 Resampling Errors (Model Based) 9.3 Influence 9.3.1 Empirical Influence Values for a Statistic 9.3.2 Jackknife-after-Bootstrap Plots 10 Permutation Tests 10.1 Introduction 10.2 Tests for Equal Distributions 10.3 Multivariate Tests for Equal Distributions 10.3.1 Nearest Neighbor Tests 10.3.2 Energy Test for Equal Distributions 10.4 Application: Distance Correlation 11 Markov Chain Monte Carlo Methods 11.1 Introduction 11.1.1 Integration Problems in Bayesian Inference 11.1.2 Markov Chain Monte Carlo Integration 11.2 The Metropolis-Hastings Algorithm 11.2.1 Metropolis-Hastings Sampler 11.2.2 The Metropolis Sampler 11.2.3 Random Walk Metropolis 11.2.4 The Independence Sampler 11.3 The Gibbs Sampler 11.4 Monitoring Convergence 11.4.1 Why Monitor Convergence 11.4.2 Methods for Monitoring Convergence 11.4.3 The Gelman-Rubin Method 11.5 Application: Change Point Analysis 12 Probability Density Estimation 12.1 Univariate Density Estimation 12.1.1 Histograms 12.1.2 Frequency Polygon Density Estimate 12.1.3 The Averaged Shifted Histogram 12.2 Kernel Density Estimation 12.3 Bivariate and Multivariate Density Estimation 12.3.1 Bivariate Frequency Polygon 12.3.2 Bivariate ASH 12.3.3 Multidimensional Kernel Methods 12.4 Other Methods of Density Estimation 13 Introduction to Numerical Methods in R 13.1 Introduction 13.2 Root-finding in One Dimension 13.3 Numerical Integration 13.4 Maximum Likelihood Problems 13.5 Application: Evaluating an Expected Value 14 Optimization 14.1 Introduction 14.2 One-dimensional Optimization 14.3 Maximum Likelihood Estimation with mle 14.4 Two-dimensional Optimization 14.5 The EM Algorithm 14.6 Linear Programming – The Simplex Method 14.7 Application: Game Theory 15 Programming Topics 15.1 Introduction 15.2 Benchmarking: Comparing the Execution Time of Code 15.2.1 Using the microbenchmark Package 15.2.2 Using the rbenchmark Package 15.3 Profiling 15.4 Object Size, Attributes, and Equality 15.4.1 Object Size 15.4.2 Attributes of Objects 15.4.3 Comparing Objects for Equality 15.5 Finding Source Code 15.5.1 Finding R Function Code 15.5.2 Methods 15.5.3 Methods and Functions in Packages 15.5.4 Compiled Code 15.6 Linking C/C++ Code Using Rcpp 15.7 Application: Baseball Data