May I put a quotation here:
If the results disagree with informed opinion, do not admit a simple logical interpretation, and do not show up clearly in a graphical presentation, they are probably wrong. There is no magic about numerical methods, and many ways in which they can break down. They are a valuable aid to the interpretation of data, not sausage machines automatically transforming bodies of numbers into packets of scientific fact.
(by F.H.C. Marriott, cited in Johnson and Wichern)
In general (mainly inference):
- Aitken A.C. Statistical Mathematics
- Balakrishnan N. and Nevzorov V.B. A Primer on Statistical Distributions
- Casella G. and Berger R.L. Statistical Inference - A standard text, sort of. Used widely in grad school.
- Efron B. and Tibshirani R.J. An Introduction to the Bootstrap
- Fisher R.A. Statistical Methods, Experimental Design, and Scientific Inference: A Re-issue of Statistical Methods for Research Workers, The Design of Experiments, and Statistical Methods and Scientific Inference
- Good P.I. Permutation, Parametric, and Bootstrap Tests of Hypotheses
- Hogg R.V., McKean J.W. and Craig A.T. Introduction to Mathematical Statistics - Classical text modernised. If you are serious about Statistics. Quite professional, not so user friendly for people from other fields. 11 pages of errata... it's a pain for customers to correct such long list of typos.
- Kardaun O.J.W.F. Classical Methods of Statistics
- Kendall M. Stuart A. and Ord J.K. Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory
- Lehmann E.L. Elements of Large-Sample Theory
- Lehmann E.L. and Casella G. Theory of Point Estimation
- Lehmann E.L. and Romano J.P. Testing Statistical Hypotheses - Classical work on hypotheses testing.
- Murray M.K. and Rice J.W. Differential Geometry and Statistics
- Pickering A. maintained by Tharp I. Statistics Teaching (FREE!) - Includes
* Review of Basic Stats Concepts and Techniques (FREE!)
* Selected Multivariate Statistical Techniques (FREE!)
* General Linear Model Techniques: (M)AN(C)OVA (FREE!)
* Miscellaneous Advanced and Non-Standard Topics (FREE!)
- Rao C.R. Linear Statistical Inference and Its Application
- Shao J. Mathematical Statistics - Note this is a measure-theoretic based text.
- Wasserman L. All of Statistics: A Concise Course in Statistical Inference - The author aimed to write a short course in this area. It's kind of encyclopedic, rather than a textbook that explains everything in detail. But if it's a handbook, it's kind of incomplete. And if you want a handbook, why don't use just get a handbook? Wasserman states in page 25 that if the reader is unfamiliar with "inf" then just treat it as the minimum. I can't accept this for if "inf" can be treated as minimum there is no point to introduce "sup" and "inf". Also, he often uses 2 instead of 1.96 for z_(0.05/2). Check the errata list.
Statistical Models and Regression:
- Cook R.D. and Weisberg S. Residuals and Influence in Regression (here for FREE!)
- DeCoster J. Applied Linear Regression Set 1, Set 2 [.pdf] (FREE!)
- Draper N. and Smith H. Applied Regression Analysis
- Fox J. Applied Regression Analysis, Linear Models, and Related Methods
- Goldstein H. Multilevel Statistical Models (FREE!)
- Graybill F.A. and Iyer H.K. Regression Analysis: Concepts and Applications (here for FREE!)
- Härdle W. Applied Nonparametric Regression (here or here [.pdf] for FREE!)
- Härdle W., Müller M., Sperlich S. and Werwatz A. Nonparametric and Semiparametric Models (here or here [.pdf] for FREE!)
- Harrell F.E.Jr. Regression Modeling Strategies
- Hosmer D.W. and Lemeshow S. Applied Logistic Regression - Ftp area here. Stata, SAS, SPSS code here.
- Jiang J. Linear and Generalized Linear Mixed Models and Their Applications
- Kendall M. Stuart A., Ord J.K. and Arnold S. Kendall's Advanced Theory of Statistics: Volume 2A -Classical Inference and and the Linear Model
- Kutner M.K., Nachtsheim C.J., Neter J. and Li W. Applied Linear Statistical Models - New edition of the old title Applied Linear Regression Models. Well explanation, with reasonably amount of illustration. Solution, data set, errata etc. for 5th ed.; for 4th ed.
- Lindsey J.K. Applying Generalized Linear Models
- McCullagh P. and Nelder J.A. Generalized Lienar Models - Standard GLM reference.
- Mendenhall W. and Sincich T.L. A Second Course in Statistics: Regression Analysis
- Rao C.R. and Toutenburg H. Linear Models: Least Squares and Alternatives
- Rao C.R., Toutenburg H., Shalabh and Heumann C. Linear Models and Generalizations: Least Squares and Alternatives
- Schroeder L., Sjoquist D.L. and Stephan P.E. Understanding Regression Analysis: An Introductory Guide
- Seber G.A. and Lee A.J. Linear Regression Analysis
- Sengupta S. and S.R. Jammalamadaka Linear Models: An Integrated Approach - Data set and solution on web.
- Song P.X.-K. Correlated Data Analysis: Modeling, Analytics, and Applications
- Tubbs J.D. Regression Lecture Notes [.pdf] (FREE!)
- Weisberg S. Applied Linear Regression
- Afifi A.A. and Clark V.A. Computer-Aided Multivariate Analysis - Uses packages: STAT, STATISTICAL, SYSTAT, BMDP, SAS and SPSS.
- Anderson T.W. An Introduction to Mulrivariate Statistical Analysis
- Bilodeau M. and Brenner D. Theory of Multivariate Statistics
- Borga M., Landelius T. and Knutsson H. A Unified Approach to PCA, PLS, MLR and CCA (FREE!)
- Härdle W. and Simar L. Applied Multivariate Statistical Analysis (here or here [.pdf] for FREE!)
- Härdle W. and Hlavka Z. Multivariate Statistics: Exercises and Solutions (here or here [.pdf] for FREE!)
- Jackson J.E. A User's Guide to Principal Components
- Johnson R.A. and Wichern D.W. Applied Multivariate Statistical Analysis - Recommended for a first course. Not so applied indeed, mind you. Data for 6th edition here, click "Take a closer look".
- Kachigan S.K. Multivariate Statistical Analysis: A Conceptual Introduction
- Lattin J., Carroll D. and Green P. Analyzing Multivariate Data
- Mardia K.V., Kent J.T. and Bibby Multivariate Analysis
- Miles D.B. and McCarthy B.C. BIOS870 Multivariate Statistics (FREE!)
- Murtagh F. and Heck A. Multivariate Data Analysis (Expanded version here [.pdf] for FREE!)
- Shlens J. A Tutorial on Principal Component Analysis or here [.pdf] (FREE!)
- Smith L.I. A Tutorial on Principal Components Analysis [.pdf] (FREE!)
- Stockburger D.W. Multivariate Statistics: Concepts, Models, and Applications (FREE!)
- Tabachnick B.G. and Fidell L.S. Using Multivariate Statistics - Check out their page for the 4th edition here and the 5th here. Uses packages: SYSTAT, SAS and SPSS.
- Tubbs J.D. Multivariate Lecture Notes [.pdf] (FREE!)
- Tucker L. and MacCallum R. Exploratory Factor Analysis (FREE!)
- Wendorf C.A. Manual for Univariate and Multivariate Statistics (FREE!)
- Albert J. Bayesian Computation with R
- Berger J.O. Statistical Decision Theory and Bayesian Analysis
- Bernardo J. M. Bayesian Statistics [.pdf] (FREE!)
- Bernardo J. M. Introduction to Objective Bayesian Statistics [.pdf] (FREE!)
- Bernardo J. M. Reference Analysis [.pdf] (FREE!)
- Bernardo J.M. and Smith A.F.M. Bayesian Theory - Motivated by de Finetti's text (listed in stage 3 probability).
- Bolstad W.M. Introduction to Bayesian Statistics
- Botje M. Introduction to Bayesian Inference (FREE!)
- Carlin B.P. and Louis T.A. Bayes and Empirical Bayes Methods for Data Analysis - Data set can be found here.
- Congdon P. Bayesian Statistical Modelling
- Gelman A., Carlin J.B., Stern H.S. and Rubin D.B. Bayesian Data Analysis - Recommended for a first course. Check out Gelman's website for extra information, including data sets, solution and errata etc. Gelman has a blog.
- Ghosh J., Delampady M. and Samanta T. An Introduction to Bayesian Analysis: Theory and Methods
- Kendall M. and O'Hagan A. Kendall's Advanced Theory of Statistics: Volume 2B: Bayesian Inference
- Koch K.-R. Introduction to Bayesian Statistics
- Koski T. Bayesian Statistics and Markov Chain Monte Carlo (FREE!)
- Robert C.P. Research Topics / Slides - Nice material. Be careful if you want to print it, pages are overlapped.
* Bayesian Statistics [.pdf] (FREE!)
* Markov Chain Monte Carlo or here [.pdf] (FREE!)
* Model Choice or here [.pdf] (FREE!)
* Theory of Probability Revisited [.pdf] (FREE!)
- Rowe D.B. Multivariate Bayesian Statistics: Models for Source Separation and Signal Unmixing
- Thornburg H. Introduction to Bayesian Statistics (FREE!)
Simulation and the Monte Carlo Method:
- Berg B.A. Introduction to Markov Chain Monte Carlo Simulations and their Statistical Analysis (FREE!)
- Casella G. Introduction to Monte Carlo Statistical Methods [.pdf] (FREE!)
- Casella G. Statistical Inference and Monte Carlo Algorithms and discussion [.pdf] (FREE!)
- Hammersley J.M. and Handscomb D.C. Monte Carlo Methods - (here [.pdf] for FREE!)
- Haugh M. Monte Carlo Simulation (FREE!)
- Rubinstein R.Y. and Kroese D.P. Simulation and the Monte Carlo Method
- Ross S.M. Simulation
- Rummukainen K. Monte Carlo Simulation Methods (FREE!)
- Sokal A.D. Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms [.ps] (FREE!)
- Conover W.J. Practical Nonparametric Statistics
- Gibbons J.D. and Chakraborti S. Nonparametric Statistical Inference
- Härdle W., Müller M., Sperlich S. and Werwatz A. Nonparametric and Semiparametric Models (here or here [.pdf] FREE!)
- Lehmann E.L. and D'Abrera H.J.M. Nonparametrics: Statistical Methods Based on Ranks
- Wasserman L. All of Nonparametric Statistics
Categorical Data Analysis:
- Agresti A. An Introduction to Categorical Data Analysis - Correction to 1st/2nd [.pdf] edition.
- Agresti A. Categorical Data Analysis - See author's website for this book, that provides datasets used for examples, solutions, etc.
- Friendly M. Categorical Data Analysis with Graphics (FREE!)
- Lloyd C.J. Statistical Analysis of Categorical Data
- Powers D.A. and Xie Y. Statistical Methods for Categorical Data Analysis
- Williams R. Categorical Data Analysis (FREE!)
- Han J. and Kamber M. Data Mining: Concepts and Techniques - PowerPoint Slides on web.
- Hastie T. Tibshirani R. and Friedman J.H. The Elements of Statistical Learning: Data Mining, Inference, and Prediction - See their web for data, errata, etc.
- Myatt G. Making Sense of Data: A Practical Guide to Exploratory Data Analysis and Data Mining
- Box G., Jenkins G.M. and Reinsel G. Time Series Analysis: Forecasting & Control
- Brillinger D.R. Time Series: Data Analysis and Theory
- Brillinger D.R. Time Series: General [.pdf] (FREE!)
- Brockwell P.J. and Davis R.A. Introduction to Time Series and Forecasting
- Brockwell P.J. and Davis R.A. Time Series: Theory and Methods
- Chair of Statistics, University of Würzburg A First Course on Time Series Analysis: Examples with SAS (FREE!)
- Chatfield C. The Analysis of Time Series: An Introduction
- Fuller W.A. Introduction to Statistical Time Series
- Hamilton J.D. Time Series Analysis
- Shumway R.H. and Stoffer D.S. Time Series Analysis and Its Applications: With R Examples - Check out the web for data, errata, etc.
Further Reading and Reference:
- Casella G. Statistical Design - Data set here.
- Dallal G.E. The Little Handbook of Statistical Practice (FREE!)
- Davidian M. Preparation for Statistical Research (FREE!)
- Fisher R.A. and Yates F. Statistical Tables for Biological, Agricultural and Medical Research [.pdf] (FREE!)
- Gentle J.E., Härdle W. and Mori Y. (ed.) Handbook of Computational Statistics (here or here [.pdf] for FREE!)
- Kish L. Statistical Design for Research
- Little R.J.A. and Rubin D.B. Statistical Analysis With Missing Data
- Ramsay J.O. and Silverman B.W. Applied Functional Data Analysis
- Ramsay J.O. and Silverman B.W. Functional Data Analysis
- Zwillinger D. and Kokoska S. CRC Standard Probability and Statistics Tables and Formulae