Statistical computing with R:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press (Taylor & Francis Group)
[2019]
|
| Edition: | Second edition |
| Series: | Chapman & Hall / CRC The R series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 474 Seiten Illustrationen, Diagramme |
| ISBN: | 9781466553323 |
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| adam_text | Contents Preface to the Second Edition Preface to the First Edition 1 Introduction 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 Statistical Computing............................................................... The R Environment .................................................................. Getting Started with R and RStudio .................................... Basic Syntax.............................................................................. Using the R Online Help System............................................. Distributions and Statistical Tests ........................................... Functions.................................................................................... Arrays, Data Frames, and Lists ............................................. Formula Specification ............................................................... Graphics .................................................................................... Introduction to ggplot ............................................................ 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 ........................................................................ xi xiii 1 1 3 5 7 9 11 12 13 20 20 23 26 28 28 31 32 33 33 37 37 42 45 49 50 51 55 57 v
vi Contents 3 Methods for Generating RandomVariables 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........................ Exercises ............................................................................................. 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 ..................................................................... Exercises
............................................................................................. 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 ............................................................... Exercises ............................................................................................ Contents 61 61 63 64 65 69 71 75 83 83 90 92 93 96 99 99 99 104 105 109 112 115 115 115 118 120 121 124 126 129 129 132 133 135 141 143 143 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 ............................................. Exercises ............................................................................................. R Code ................................................................................................ 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............... Exercises ............................................................................................. 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 BootstrapConfidence 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................................................... vii 147 147 147 148 152 154 155 159 162 163 163 168 173 176 178 181 183 183 184 184 185 188 192 193 197 200 204 209
213 213 215 217 220 224 224 225 226 228 231 235
viii Contents Contents Exercises ................................................................................................ 9 Resampling Applications 9.1 9.2 Jackknife-after-Bootstrap........................................................... 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..................................... Exercises ................................................................................................ 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 ........................................... Exercises ................................................................................................ 11 Markov Chain Monte Carlo Methods 239 243 243 246 250 254 260 260 261 263 265 265 269 272 273 281 287 294 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..................................... Exercises ................................................................................................ R Code.................................................................................................... 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............................ Exercises ................................................................................................ 337 337 338 345
347 351 361 361 364 366 369 370 373 375 375 383 386 391 394 398 297 14 Optimization 11.1 Introduction ................................................................................. 11.1.1 Integration Problems in BayesianInference................. 11.1.2 Markov Chain MonteCarlo 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 ........................................ Exercises ................................................................................................ R Code................................................................................................... ix 297 297 298 299 300 310 310 316 318 322 322 323 323 327 333 335 14.1 Introduction ................................................................................. 14.2 One-dimensional Optimization
.................................................. 14.3 Maximum Likelihood Estimation with mie ............................ 14.4 Two-dimensional Optimization.................................................. 14.5 The EM Algorithm .................................................................... 14.6 Linear Programming - The Simplex Method ......................... 14.7 Application: Game Theory ........................................................ Exercises ................................................................................................ 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........................................................ 401 401 402 403 405 409 411 413 417 419 419 419 420 423 425 427 427 428
x Contents 15.4.3 Comparing Objects for Equality ................................. 15.5 Finding Source Code ............................................................... 15.5.1 Finding R FunctionCode.............................................. 15.5.2 Methods........................................................................... 15.5.3 Methods and Functionsin Packages............................ 15.5.4 Compiled Code............................................................... 15.6 Linking C/C++ Code Using Repp.......................................... 15.7 Application: Baseball Data ...................................................... Exercises ............................................................................................ 429 430 430 431 432 433 434 438 442 Notation 445 Bibliography 447 Index 469
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| spelling | Rizzo, Maria L. Verfasser (DE-588)1089584350 aut Statistical computing with R Maria L. Rizzo Second edition Boca Raton ; London ; New York CRC Press (Taylor & Francis Group) [2019] xiv, 474 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Chapman & Hall / CRC The R series Dataprocessing gtt Estadística matemática Programmeertalen gtt R (computerprogramma) gtt Statistiek gtt Datenverarbeitung Statistik Mathematical statistics Data processing Statistics Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 s R Programm (DE-588)4705956-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4665-5333-0 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028450217&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rizzo, Maria L. Statistical computing with R Dataprocessing gtt Estadística matemática Programmeertalen gtt R (computerprogramma) gtt Statistiek gtt Datenverarbeitung Statistik Mathematical statistics Data processing Statistics Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd Statistische Analyse (DE-588)4116599-8 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4116599-8 |
| title | Statistical computing with R |
| title_auth | Statistical computing with R |
| title_exact_search | Statistical computing with R |
| title_full | Statistical computing with R Maria L. Rizzo |
| title_fullStr | Statistical computing with R Maria L. Rizzo |
| title_full_unstemmed | Statistical computing with R Maria L. Rizzo |
| title_short | Statistical computing with R |
| title_sort | statistical computing with r |
| topic | Dataprocessing gtt Estadística matemática Programmeertalen gtt R (computerprogramma) gtt Statistiek gtt Datenverarbeitung Statistik Mathematical statistics Data processing Statistics Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd Statistische Analyse (DE-588)4116599-8 gnd |
| topic_facet | Dataprocessing Estadística matemática Programmeertalen R (computerprogramma) Statistiek Datenverarbeitung Statistik Mathematical statistics Data processing Statistics Data processing R (Computer program language) R Programm Statistische Analyse |
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