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CASt online resources

Broad coverage of statistics in single volumes

Undergraduate level
Mathematical statistics and data analysis
    by John A. Rice (3rd ed, 2006). Mathematical statistics textbook interwoven with applications and practice. Covers probability, statistical distributions, central limit theorem, survey sampling. parameter estimation, hypothesis testing, goodness-of-fit, data visualization, two-sample comparisons, bootstrap, analysis of variance, categorical data, linear least squares, Bayesian inference and decision theory.

    by David Freeman, Robert Pisani & Roger Purves (3rd ed, 1998). Popular and well-written elementary textbook deemphasizing mathematical formulae. Covers experiment design, descriptive statistics, correlation & regression, probability, sampling, measurement error, and tests of significance.

Advanced Statistics from an Elementary Point of View
    by Michael J. Panik (2005). Broad, readable textbook covering descriptive statistics, random variables and probability distributions, sampling, maximum likelihood and point estimation, parametric hypothesis tests, nonparametric techniques, goodness-of-fit, bivariate correlation and regression.

Introductory Statistics and Random Phenomena
    by Manfred Denker & Wojbor A. Woyczynski (1998). Textbook designed for engineering students emphasizing stochastic processes. Covers descriptive statistics, distributions, randomness, chaos, maximum-likelihood modeling, modeling normal populations, and ANOVA.

100 Statistical Tests
    by Gopal K. Kanji (3rd ed, 2006). Concise, popular handbook presenting standard tests (mostly for normal populations) covers tests of correlation, 2- and k-sample tests, median and rank tests, and autocorrelation tests. Includes chi-squared, Cochran, delta, Dixon, Duckworth, Dunnett, Durbin-Watson, F, Fisher, H, Harrison, Hartley-Kanji-Gadsden, Kendall, Kolmogorov-Smirnov, Kruskal-Wallis, Link-Wallis, Mardia-Watson-Wheeler, median, q, Q, rank, run, sequential, serial correlation, Siegel-Tukey, sign, Spearman, Steel, t, Tukey, U, UMP, V, w/s, Watson-Williams, Watson U, Wilcoxon, Wilcoxon-Wilcox, Wilcoxon-Mann-Whitney, and Z tests.

Common Errors in Statistics and How to Avoid Them
    by Phillip I. Good & James W. Hardin (2nd ed, 2006). Readable, informal introduction to statistical procedures. Includes basic concepts, hypothesis testing and estimation, p-values and confidence intervals, graphics, model selection, regression methods, multivariate regression, and model validation.

Graduate level
Introduction to mathematical statistics
    by Robert Hogg, Joseph McKean & Allen Craig (6th ed, 2005). Graduate-level survey of mathematical statistics with a strong mathematical component. Covers probability & distributions, convergence, confidence intervals, Monte Carlo and bootstrap, maximum likelihood methods, EM Algorithm, sufficiency, optimal hypothesis tests, ANOVA and normal models, nonparametric statistics, Bayesian statistics, linear models (robust, least squares, Wilcoxon, general).

Essentials of Statistical Inference
    by G. A. Young and R. L. Smith (2005). Slim text developed at the University of Cambridge with emphasis on computational techniques (e.g. bootstrap, MCMC). Includes Bayesian methods and decision theory, hypothesis testing, sufficiency, confidence sets, likelihood theory, prediction, bootstrap methods, and other topics (e.g. pseudo-likelihoods, Edgeworth expansion, Bayesian asymptotics).

All of statistics: A concise course in statistical inference
    by Larry Wasserman (2004). Intended for graduate students in allied fields, this book gives a presentation of a wide range of topics with emphasis on mathematical background and theorems. Topics include random variables, expectations, empirical distribution functions, bootstrap, maximum likelihood, hypothesis testing, Bayesian inference, linear and loglinear models, multivariate models, graphs, density estimation, classification, stochastic processes and simulation methods. Web page provides R code and datasets.

Principles of Statistical Inference
    by D. R. Cox (2006). A slim volume by a distinguished statistician, this gives a discursive, fairly advanced, presentation of fundamental issues including comparison of frequentist and Bayesian approaches. Topics include interpretations of uncertainty, significant tests, asymptotic theory, aspects of maximum likelihood.

Comparative Statistical Inference
    by Vic Barnett (3rd ed, 1999). Detailed and well-written comparison of three approaches in modern statistics: classical frequentist, Bayesian, and decision theoretical. Includes illustration of the approaches, views of probability, utility and decision-making, and other approaches to inference (e.g. fiducial, structural).

Statistical Models
    by A. C. Davison (2003). A thick textbook with examples in R covering topics including confidence intervals, likelihood and model selection, stochastic models, point and Poisson processes, estimation and hypothesis testing, linear and nonlinear regression models, Bayesian models, conditional and marginal inference.

Testing Statistical Hypotheses and Theory of Point Estimation
    by E. L. Lehmann & Joseph P. Romano (3rd ed, 2005) and by E. L. Lehmann & George Casella (2nd ed, 1998). Lehmann's classic, comprehensive graduate texts in mathematical statistics from the 1980s. Covers probability, unbiased tests, linear hypotheses (including chi-squared), minimax principle, conditional inference, Bayes estimation, large-sample theory, asymptotic optimality.

Mathematical statistics: basic ideas and selected topics
    by Peter J. Bickel, Kjell A. Doksum (2nd ed, 2001).

Stochastic modelling of scientific data
    by Guttorp, Peter (2001).
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