
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, goodnessoffit, data visualization, twosample comparisons, bootstrap, analysis of variance, categorical data, linear least squares, Bayesian inference and decision theory.
Statistics
by David Freeman, Robert Pisani & Roger Purves (3rd ed,
1998). Popular and wellwritten 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, goodnessoffit, 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, maximumlikelihood 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 ksample tests, median and rank tests, and autocorrelation tests. Includes chisquared, Cochran, delta,
Dixon, Duckworth, Dunnett, DurbinWatson, F, Fisher, H, Harrison,
HartleyKanjiGadsden, Kendall, KolmogorovSmirnov, KruskalWallis,
LinkWallis, MardiaWatsonWheeler, median, q, Q, rank, run, sequential,
serial correlation, SiegelTukey, sign, Spearman, Steel, t, Tukey, U, UMP, V,
w/s, WatsonWilliams, Watson U, Wilcoxon, WilcoxonWilcox,
WilcoxonMannWhitney, 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, pvalues 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). Graduatelevel 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. pseudolikelihoods, 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 wellwritten comparison of three approaches in modern statistics: classical frequentist, Bayesian, and decision theoretical. Includes illustration of the approaches, views of probability, utility and decisionmaking, 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 chisquared), minimax principle,
conditional inference, Bayes estimation, largesample 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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