Statistics 375 Mathematical Statistics

Textbook

R Programming for Chihara and Hesterberg's Mathematical Statistics with Resampling and R

Laura Chihara and Tim Hesterberg make available on their web site a comprehensive collection of files illustrating the use of the R programming language in support of their course. The following scripts used those files as their starting points, and added a few pirouettes and swirls that I managed to dream up while working through the material. The alert reader could decipher which are the contributions of the book's authors and which are mine by a simple line-by-line textual analysis of the original files which are available online and the modified ones which are here, but the bottom line is that virtually all of the leadership was provided by the authors, and the following scripts are products of an appreciative student working at absorbing this material. These notes do not contain the solutions to any of the exercises in their text.

• 1. Data and Case Studies (R script)
• 2. Exploratory Data Analysis (R script)
• 3. Hypothesis Testing (R script)
• 4. Sampling Distributions (R script)
• 5. The Bootstrap (R script)
• 6. Estimation (R script)
• 7. Classical Inference : Confidence Intervals (R script)
• 8. Classical Inference : Hypothesis Testing (R script)
• 9. Regression (R script)
• 10. Bayesian Methods (R script)
• 11. Additional Topics

R Programming for Efron and Tibshirani's An Introduction to the Bootstrap

Bradley Efron and Robert Tibshirani's An Introduction to the Bootstrap is a marvelous introduction to wide swaths of modern statistics. Fresh and engaging, the examples and discussions create energy and excitement in the exploring student. It is a fine bridge to the survey of much of contemporary statistics presented in Carl Morris and Robert Tibshirani's The Science of Bradley Efron: Selected Papers.

• 1. Introduction (R script, aspirin.r)
• 2. The Accuracy of a Sample Mean (R script, mouse.r)
• 3. Random Samples and Probabilities (R script)
• 4. The Empirical Distribution Function and the Plug-In Principle
• 5. Standard Errors and Estimated Standard Errors
• 6. The Bootstrap Estimate of Standard Error (R script)
• 7. Bootstrap Standard Errors: Some Examples (R script)
• 8. More Complicated Data Structures (R script)
• 9. Regression Models (R script)
• 10. Estimates of Bias (R script)
• 11. The Jackknife (R script)
• 12. Confidence Intervals Based on Bootstrap "Tables" (R script)
• 13. Confidence Intervals Based on Bootstrap Percentiles
• 14. Better Bootstrap Confidence Intervals
• 15. Permutation Tests
• 16. Hypothesis Testing with the Bootstrap
• 17. Cross-Validation and Other Estimates of Prediction Error
• 18. Adaptive Estimation and Calibration
• 19. Assessing the Error in Bootstrap Estimates
• 20. A Geometrical Representation for the Bootstrap and Jackknife
• 21. An Overview of Nonparametric and Parametric Inference
• 22. Further Topics in Bootstrap Confidence Intervals
• 23. Efficient Bootstrap Computations
• 24. Approximate Likelihoods
• 25. Bootstrap Bioequivalence
• 26. Discussion and Further Topics
• Appendix: Software for Bootstrap Computations
• References

R Programming for Faraway's Linear Models with R

The following notes take full-scale advantage of the chapter-by-chapter transcripts available on the author's web site.

• Introduction (R script)
• Estimation (R script)
• Inference (R script)
• Diagnostics
• Problems with the Predictors
• Problems with the Error
• Transformation
• Variable Selection
• Shrinkage Methods
• Statistical Strategy and Model Uncertainty
• Insurance Redlining - A Complete Example
• Missing Data
• Analysis of Covariance
• One way ANOVA
• Factorial Designs
• Block Designs

R Programming for Larsen and Marx's Introduction to Mathematical Statistics and Its Applications, 5/E

• 11. Regression (R script)
• 12. The Analysis of Variance (R script, smokers.csv)
• 13. Randomized Block Designs

R Programming for DeGroot and Schervish's Probability and Statistics, Fourth Edition

• 11. Linear Statistical Models (R script)

References

• View the book on Google books.
• Data files, errata, and software supporting this text are available from the StatLib archive at Carnegie Mellon University. Log into statlib with the username "statlib" and search for the file "bootstrap.funs." Follow the enclosed directions to unpack the file with the shell command "sh bootstrap.funs"
• The R package "bootstrap" in support of this book is available on cran, but note that it recommends that new projects use the package "boot".
• Bradley Efron's home page.
• Robert Tibshirani's home page.
• Some related references.
  

Professor