• Ash R.B. Lectures on Statistics (FREE!)
• Bain L.J. and Engelhardt M. Introduction to Probability and Mathematical Statistics 
• DeGroot M.H. and Schervish M.J. Probability and Statistics - Detail explanation. Common misconceptions are mentioned, for example: "Probability Zero Does Not Mean Impossible" (p.17) and Statistical Swindles (p.45). Check out the typo page.
• Garthwaite P.H., Jolliffe I.T. and Jones B. Statistical Inference - Made a few good comments, but perhaps too concise as a textbook. Can be served as a reference. Unlike the rest recommended texts for this course, stage 2 probability and statistics is the assumed knowledge for this text.
• Lebanon G. Tutorial Notes (FREE!) - Read S1 - S12.
• Lowry R. Concepts and Applications of Inferential Statistics (FREE!)
• Mood A.M., Graybill F.A. and Boes D.C. Introduction to the Theory of Statistics - As my lecturer Spiridon Penev have said, this text is a bit outdated but it contains useful exercise problems. 
• Mukhopadhyay N. Probability and Statistical Inference 
• Rice J.A. Mathematical Statistics and Data Analysis - The main feature of this book is that it contain lots of figures. Check the errata.
• Roussas G.G. A Course in Mathematical Statistics 
• Roussas G.G. An Introduction to Probability and Statistical Inference 
• Sprott D.A. Statistical Inference in Science 
• Wald A. On the Principles of Statistical Inference (FREE!)
• Weber R. Statistics [.pdf] (FREE!)
• Young G.A. and Smith R.L. Essentials of Statistical Inference - A bit advanced for a first course, perhaps.

• Baclawski K. and Rota G.-C. An Introduction to Probability and Random Processes [.pdf] (FREE!)
• de Finetti B. Theory of Probability: A Critical Introductory Treatment - The author is notable for "operational subjective".
• Feller W. An Introduction to Probability Theory and Its Applications Vol. 1 - "A colorful and rich introduction to probability theory and its applications" according to Karlin and Taylor, but it "is limited in that it deals only with discrete probabilities."
• Gray R.M. and Davisson L.D. Introduction to Statistical Signal Processing (FREE!)
• Grimmett G.R. and Stirzaker D.R. Probability and Random Processes 
• Hsu H. Schaum's Outline of Probability, Random Variables, and Random Processes 
• Kao E.P.C. An Introduction to Stochastic Processes 
• Karlin S. and Taylor H.M. A First Course in Stochastic Processes 
• Krishnan V. Probability and Random Processes 
• Lebanon G. Tutorial Notes (FREE!) - Read R1 - R5.
• Mörters P. Lecture Notes on Probability Theory [.ps] (FREE!)
• Papoulis A. Probability, Random Variables and Stochastic Processes - See their web for resources.
• Ross S.M. Introduction to Probability Models - Note this is an introduction to probability and stochastic processes, not an introduction to basic probability theory. This text could be quite hard to follow without knowing very basic probability theory. Also note that, no graph has been used when the author introduce Markov chains for the first time.
• Walrand J. Lecture Notes on Probability Theory and Random Processes [.pdf] (FREE!)
• Yates R.D. and Goodman D.J. Probability and Stochastic Processes: An Friendly Introduction for Electrical and Computer Engineers 

Probability (optional):
These days, studying probability without measure is like studying physics without calculus. If you have done some baby measure theory in stage 3, you are probably ready for the followings.

Check out Probability Theory As Extended Logic for collected probability papers.

Probaility built upon Measure Theory:

• Ash R.B. and Doleans-Dade C.A. Probability & Measure Theory  
• Athreya K.B. and Lahiri S.N. Measure Theory and Probability Theory 
• Bass R.F. Probability Theory [.pdf] (FREE!)
• Billingsley P. Convergence of Probability Measures 
• Billingsley P. Probability and Measure 
• Bobrowski A. Functional for Analysis for Probability and Stochastic Processes: An Introduction 
• Capinski M. and Kopp P.E. Measure, Integral and Probability 
• Chung K.L. A Course in Probability Theory
• Dembo A. Probability Theory [.pdf] (FREE!)
• Dudley R.M. Real Analysis and Probability 
• Feller W. An Introduction to Probability Theory and Its Applications Vol. 2
• Gnedenko B.V. and Kolmogorov A.N. Limit Distributions for Sums of Independent Random Variables 
• Gray R.M. Probability, Random Processes, and Ergodic Properties (FREE!)
• Gut A. Probability: A Graduate Course 
• Jaynes E.T. Probability Theory: The Logic of Science (here for FREE!)
• Jorgensen P.E.T. Analysis and Probability: Wavelets, Signals, Fractals 
• Kallenberg O. Foundations of Modern Probability - Nice historical and bibliographical notes are included at the back.
• Knill O. Probability and Stochastic Processes with Applications [.pdf] (FREE!)
• Loève M. Probability Theory I, II - Fairly comprehensive.
• Kolmogorov A.N. Foundations of the Theory of Probability (FREE!) - For historical interest.
• Shiryaev A.N. Probability - The material is based on a three-semester course of lectures, under the title Probability, Statistics, Stochastic Processes, I, II, given by the author in the Moscow State University. He draws nice comparison between set-theoretic interpretation and interpretation in probability theory, see p.136-137.
• Strasser H. Introduction to Probability Theory and Stochastic Processes [.pdf] (FREE!)
• Tsirelson B. Advanced Probability Theory (FREE!)
• Wilde I.F. Measures, Integration and Probability (FREE!)
• Williams D. Probability with Martingales 

Stochastic Processes:

• Brzezniak Z. and Zastawniak T. Basic Stochastic Processes 
• Doob J.L. Stochastic Processes - Considered to be classics in the field.
• Dembo A. Stochastic Processes [.pdf] (FREE!)
• Jacod J. and Shiryaev A.N. Limit Theorems for Stochastic Processes 
• Karlin S. and Taylor H.M. A Second Course in Stochastic Processes - Amazon user Yan Zhang comments that this is a must-have if you wanna go to Wall Street.
• Mörters P. and Peres Y. Brownian Motion [.pdf] (FREE!)
• Parzen E. Stochastic Processes 
• Ross S.M. Stochastic Processes - See also Russell Lyons' course notes [.pdf].
• Shalizi S. Stochastic Processes (FREE!)
• Todorovic P. An Introduction to Stochastic Processes and Their Application 
• van Zanten H. An Introduction to Stochastic Processes in Continuous Time [.pdf] (FREE!)
• Varadhan S.R.S. Stochastic Processes (FREE!)

Stochastic Analysis:

• Bain A. Stochastic Calculus (FREE!)
• Chung K.L. and Williams R.J. An Introduction to Stochastic Integration 
• Evans L.C. An Introduction to Stochastic Differential Equations [.pdf] (FREE!) - Evans wrote a popular book on PDE.
• Karatzas I. and Shreve S.E. Brownian Motion and Stochastic Calculus 
• Klebaner F.C. Introduction to Stochastic Calculus with Applications 
• Kurtz T.G. Lectures on Stochastic Analysis [.pdf] (FREE!)
• Malliavin P. Stochastic Analysis 
• Mörters P. Lecture Notes on Stochastic Analysis [.ps] (FREE!)
• Seppalainen T. Basics of Stochastic Analysis (FREE!)
• Varadhan S.R.S. Stochastic Analysis (FREE!)
• Wilde I.F. Stochastic Analysis (FREE!)

Statistics (optional):
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. 
• 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.
• 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:

• 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 
• Graybill F.A. and Iyer H.K. Regression Analysis: Concepts and Applications (here for FREE!)
• Goldstein H. Multilevel Statistical Models (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 
• 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 
• 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  

Multivariate Analysis:

• Afifi A.A. and Clark V.A. Computer-Aided Multivariate Analysis - Uses packages: STAT, STATISTICAL, SYSTAT, BMDP, SAS and SPSS.
• 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!)

Bayesian Statistics:

• 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!)

Nonparametric Statistics:

• 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!)

Data Mining:

• 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  

Time Series:

• Box G., Jenkins G.M. and Reinsel G. Time Series Analysis: Forecasting & Control 
• 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 Firset Course on Time Series Analysis: Examples with SAS (FREE!)
• Chatfield C. The Analysis of Time Series: An Introduction 

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!)

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 
• 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 
  

[此贴子已经被作者于2008-5-2 2:32:24编辑过]

好啊