Statistics 375

Mathematical Statistics


Textbook


Mathematical Statistics with Resampling and R,
by Laura Chihara and Tim Hesterberg,
Wiley, 2011, ISBN: 978-1-118-02985-5

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.


An Introduction to the Bootstrap,
by Bradley Efron and Robert J. Tibshirani,
Chapman & Hall/CRC, 1994, ISBN: 0-412-04231-2

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.


Linear Models with R,
by Julian J. Faraway,
Chapman & Hall/CRC, 2005, ISBN: 1-58488-425-8

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 to Mathematical Statistics and Its Applications, 5/E,
by Richard J. Larsen and Morris L. Marx,
Pearson, 2012, ISBN-10: 0321693949

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



Probability and Statistics, Fourth Edition,
by Morris H. DeGroot and Mark J. Schervish,
Addison-Wesley, 2012, ISBN: 978-0-321-50046-5

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


References

large-scale inference
Efron, Bradley, 2005, Bayesians, Frequentists, and Scientists, Journal of the American Statistical Association. March 1, 2005, 100(469): 1-5.
Efron, Bradley, 2010, Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction, Institute of Mathematical Statistics Monographs. Cambridge University Press.
Efron, Bradley, Winter 2009/2010, Stats 329, Large-Scale Simultaneous Inference, and accompanying data sets and programs. Read the Foreward for a concise introduction to this Stanford statistics course taught by Bradley Efron.

false discovery rate
Benjamini and Hochberg, 1995, Controlling the false discovery rate: a practical and powerful approach to multiple testing
Efron and Tibshirani, 2002, Empirical Bayes methods and false discovery rates for microarrays

bootstrap
Efron, Bradley, 1979, Bootstrap Methods: Another Look at the Jackknife, The Annals of Statistics, Volume 7, Number 1 (1979), 1-26. Open access. Click on "PDF file."
Efron, Bradley, 1987, The Jackknife, the Bootstrap, and Other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics. Society for Industrial Mathematics.
Efron, Bradley, and Robert J. Tibshirani, 1991, Statistical Data Analysis in the Computer Age, Science 12 July 1991: Vol. 253, no. 5018, pp. 390-395
Efron, Bradley, and Robert J. Tibshirani, 1994, An Introduction to the Bootstrap, Chapman & Hall/CRC. Morris, Carl, and Robert Tibshirani (editors), 2008, The Science of Bradley Efron: Selected Papers, Springer

statistical learning
Hastie, Trevor, Robert Tibshirani, and Jerome Friedman, 2009, The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Second Edition. Springer. A pdf of the book is available from this site, by arrangement with the publisher. Preface to first (2001) and second (2009) editions. Book review of the first edition.

bayesian methods
Albert, Jim, 2009, Bayesian Computation with R (Use R!), 2nd ed., Springer. See the author's website.
Robert, Christian, and George Casella, 2009, Introducing Monte Carlo Methods with R (Use R!), Springer. Publisher's web page.
Hoff, Peter D., 2009, A First Course in Bayesian Statistical Methods, Springer Texts in Statistics. Author's web site and the book's web site.
Gelman, Andrew, John B. Carlin, Hal S. Stern, Donald Rubin, 2003, Bayesian Data Analysis, Second Edition, Chapman & Hall/CRC Texts in Statistical Science
Carlin, Bradley P., and Thomas A. Louis, 2008, Bayesian Methods for Data Analysis, Third Edition, Chapman & Hall/CRC Texts in Statistical Science.
Casella, George, 1985, An Introduction to Empirical Bayes Data Analysis, The American Statistician, Vol. 39, No. 2 (May, 1985), pp. 83-87

regression
Faraway, Julian J., 2002, Practical Regression and Anova using R (available from CRAN)
Faraway, Julian J., 2005, Linear Models with R, Chapman & Hall/CRC. Author's web site. Publisher's web site
Faraway, Julian J., 2006, Extending the Linear Model with R. Generalized Linear, Mixed Effects and Nonparametric Regression Models, Chapman & Hall/CRC. Author's web site. Publisher's web site
Fox, John, and Sanford Weisberg, 2011, An R Companion to Applied Regression, 2nd Edition, Sage Publications, Inc.

classical theory of statistics
Fisher, R. A., 1922, On the mathematical foundations of theoretical statistics, with commentary by Seymour Geisser, 1992, in Breakthroughs in Statistics: Foundations and basic theory, by Samuel Kotz and Norman Lloyd Johnson, Springer
R. A. Fisher -- A Guide to R. A. Fisher
Erich Lehmann -- In Memoriam; DeGroot, A conversation with Erich Lehmann (full text, open access; click on "PDF file"); Willem R van Zwet, Remembering Erich Lehmann

graphics
Wickham, Hadley, 2009, ggplot2. Elegant Graphics for Data Analysis, Springer. Author's web site and the ggplot2 web site
Sarkar, Deepayan, 2008, Lattice. Multivariate Data Visualization with R, Springer. Author's web site and the book's web site
Murrell, Paul, 2011, R Graphics, CRC Press, Taylor and Francis Group, Chapman & Hall

statistics with R
Venables, W. N., and B. D. Ripley, 2010, Modern Applied Statistics with S, Fourth Edition, Statistics and Computing, Springer
Dalgaard, Peter, 2008, Introductory Statistics with R, Second Edition, Statistics and Computing, Springer
Verzani, John, 2005, Using R for Introductory Statistics, Chapman and Hall/CRC

mathematical statistics
MIT OpenCourseWare 18.443 Statistics for Applications, F2003
MIT OpenCourseWare 18.443 Statistics for Applications, F2006
MIT OpenCourseWare 18.443 Statistics for Applications, S2009

software
Recommended software for biostatistics at Vanderbilt

videos
Kahn Academy, Statistics course

Professor

Chris Parrish
Office: Woods Laboratories 120
email: cparrish@sewanee.edu



cparrish@sewanee.edu