[SOLVED] Text in statistical theory?

I'm looking for a good text in statistical theory... does anyone have recommendations?

A bit about myself and what I'm looking for: I'm a PhD candidate in physics - so I have a strong math background - working on projects related to cognitive science. I've looked into some social/behavioral stats texts, but found them light on theoretical underpinnings. I suppose what I am looking for is a text appropriate for an advanced undergraduate or introductory graduate course in statistical theory.

Thanks!

If you are looking for a text with basic probability and statistical tests, then I highly recommend "Applied Statistics and Probability for Engineers" by Montgomery and Runger. see e.g http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471745898.html

In my opinion, a good balance between theory and practical applications (using "S" o "R", the later is especially suited for doing research) is "Modern Applied Statistics with S". Fourth Edition by W. N. Venables and B. D. Ripley. Springer. ISBN 0-387-95457-0, 2002.

Some Contents: 5. Univariate statistics 6. Linear statistical models 7. Generalized linear models 8. Non-linear and smooth regression 9. Tree-based methods 10. Random and mixed effects 11. Exploratory multivariate analysis 12. Classification 13. Survival analysis 14. Time series analysis 15. Spatial statistics 16. Optimization

I think it could be a very interesting first step.

Regards,

Mauricio

hzambran_cl said: In my opinion, a good balance between theory and practical applications (using "S" o "R", the later is especially suited for doing research) is "Modern Applied Statistics with S". Fourth Edition by W. N. Venables and B. D. Ripley. Springer. ISBN 0-387-95457-0, 2002.

I have to disagree. It is extremely good book if you already know statistics. It is not for novices at all.

Personally I found "Introduction to Mathematical Statistics" by Hogg and Craig to be extremely helpful for my PhD comprehensive exam. But it is probably way to mathematical, and doesn't really have good examples. Try "Statistical Inference" by Berger and Castella.

To overwhelm you in information :-). About a year ago I had a co-op who asked for books recommendation for statistician, and I compiled following list (by no means complete :-)). I hope it will be useful for anyone interested in statistics

Probability Probability by A.N. Shiryaev

An Introduction to Probability Theory and Its Applications, Volume 1 by William Feller

An Introduction to Probability Theory and Its Applications, Volume 2 by William Feller

A Course in Probability Theory Revised by Kai Lai Chung

Probability and Measure, by Patrick Billingsley

[B] Basic Statistics[/B] How to Lie With Statistics by Darrell Huff and Irving Geis

Statistical Inference by George Casella and Roger L. Berger

Common Errors in Statistics (and How to Avoid Them) by Phillip I. Good and James W. Hardin

Mathematical Statistics by Jun Shao

The Elements of Graphing Data by William S. Cleveland

Visualizing Data by William S. Cleveland

Handbook of Parametric and Nonparametric Statistical Procedures, by David J. Sheskin

Statistical Rules of Thumb by Gerald van Belle

[B] Advanced Statistics[/B] Testing Statistical Hypotheses (Springer Texts in Statistics) by E.L. Lehmann and Joseph P. Romano

Nonparametrics: Statistical Methods Based on Ranks by Erich L. Lehmann and H.J.M. D'Abrera

Theory of Point Estimation (Springer Texts in Statistics) by E.L. Lehmann and George Casella

Elements of Large-Sample Theory (Springer Texts in Statistics) by E.L. Lehmann

The Elements of Statistical Learning by T. Hastie, R. Tibshirani, and J. H. Friedman

Generalized Linear Models, Second Edition (Monographs on Statistics and Applied Probability) by P. McCullagh

An Introduction to the Bootstrap by Bradley Efron and R.J. Tibshirani

Bootstrap Methods and Their Application by A. C. Davison and D. V. Hinkley

Monte Carlo Statistical Methods by Christian P. Robert and George Casella

Optimal Statistical Decisions by Morris H. DeGroot

Statistical Decision Theory and Bayesian Analysis by James O. Berger

Bayesian Data Analysis, by Andrew Gelman, John B. Carlin, Hal S. Stern, and Donald B. Rubin

Bayesian Forecasting and Dynamic Models by Mike West and Jeff Harrison

Practical Nonparametric Statistics, by W. J. Conover

Density Estimation for Statistics and Data Analysis by Bernard. W. Silverman

Order Statistics by Herbert A. David

Robust Statistics by Peter J. Huber

Generalized Additive Models by T.J. Hastie , R.J. Tibshirani

Regression Modeling Strategies by Frank E. Jr. Harrell

Linear Regression Analysis by George A. F. Seber and Alan J. Lee

Nonlinear Regression by George A. F. Seber , C. J. Wild

Sampling Techniques by William G. Cochran

Survey Sampling by Leslie Kish

Principal Component Analysis by I.T. Jolliffe

Functional Data Analysis by J. Ramsay and B. W. Silverman

Applied Functional Data Analysis by J.O. Ramsay , B.W. Silverman

An Introduction to Multivariate Statistical Analysis by T. W. Anderson

Statistics for Spatial Data by Noel A. C. Cressie

Introduction to Time Series and Forecasting by Peter J. Brockwell and Richard A. Davis

Time Series: Theory and Methods by Peter J. Brockwell and Richard A. Davis

Time-Series Forecasting by Chris Chatfield

Time Series Analysis: Forecasting & Control by George Box, Gwilym M. Jenkins, and Gregory Reinsel

Reliability Theory and Practice by Igor Bazovsky (DOVER)

Statistical Theory of Reliability and Life Testing: Probability Models By Richard E. Barlow, Frank Proschan

System Reliability Theory: Models, Statistical Methods, and Applications, by Marvin Rausand, Arnljot Høyland

Statistics of Extremes by E. J. Gumbel

Statistics of Extremes: Theory and Applications by Jan Beirlant, Yuri Goegebeur, Johan Segers, and Jozef Teugels

Sequential Analysis by Abraham Wald (DOVER)

Multiple Comparisons: Theory and Methods by Jason Hsu

Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons by Robert E. Bechhofer , et al.

A Probabilistic Theory of Pattern Recognition by Luc Devroye , et al.

Experiments: Planning, Analysis, and Parameter Design Optimization by C. F. Jeff Wu and Michael Hamada

Design and Analysis of Experiments by Douglas C. Montgomery

Introduction to Statistical Quality Control by Douglas C. Montgomery

Statistical Quality Control by M. Jeya Chandra

Information Theory and Statistics by Solomon Kullback (DOVER)

Stochastics

Introduction to Stochastic Processes by Paul Gerhard Hoel, Sidney C. Port, and Charles J. Stone

Stochastic Processes (Wiley Classics Library) by J. L. Doob

Brownian Motion and Stochastic Calculus by Ioannis Karatzas and Steven E. Shreve

Stochastic Calculus for Finance I: The Binomial Asset Pricing Modelby Steven E. Shreve

Stochastic Calculus for Finance II: Continuous-Time Models by Steven E. Shreve Methods of Mathematical Finance by Ioannis Karatzas , Steven E. Shreve

Stochastic Differential Equations: An Introduction with Applications by Bernt Oksendal

Applied Probability Models with Optimization Applications by Sheldon M. Ross (DOVER)

Introduction to Probability Models by Sheldon M. Ross (get older edition 5 or 6)

great list! brings back great memories! whenever in doubt read Feller or Doob. as the kids nowadays would say: they rule! :)

hzambran_cl said: In my opinion, a good balance between theory and practical applications (using "S" o "R", the later is especially suited for doing research) is "Modern Applied Statistics with S". Fourth Edition by W. N. Venables and B. D. Ripley. Springer. ISBN 0-387-95457-0, 2002.

I think it could be a very interesting first step.

I don't recommend this book as first step either. As the authors put it *"Readers are assumed to have a basic grounding in statistics, and so the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics."*

However, _after you have learned the basics_ this is a great book, that I find myself resorting to almost daily when working with data.

If you want to learn R (which is always a good idea :) ) at the same time as statistics you might consider: "Introductory Statistics with R, 2nd edition by Peter Dalgaard http://staff.pubhealth.ku.dk/~pd/ISwR.html

Thanks for your help. I recently came to the same conclusion.

I am already an R user, so it seemed like a good choice!

ahmatti said: I don't recommend this book as first step either. As the authors put it *"Readers are assumed to have a basic grounding in statistics*

Thanks for your reply and the one of 'Tart', pointing out that for reading this book you need a basic grounding in statistics, because when I mention this book as a good first step, I did it in the context of original question, a PhD candidate in physics looking for good text in statistical theory, and I assumed that the basic grounding in statistics was present.

ahmatti said: the book is intended for would-be users of S-PLUS or R and both students and researchers using statistics."[/I]

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That is completely true, and I think that putting your hands in practical examples while you read the theory (using a software that you can download for free from internet) is a good way to grasp the concepts.

Enjoy the lecture !