Stage 3 Statistical Inference

Statistical Inference (optional):
Build upon stage 2 statistics, you will learn here the Cramer-Rao bound, uniform minimum variance unbiased estimators, Neyman-Pearson theory, Bayesian inference, basic bootstrap and robustness, introductory non-parametric (including the sign test, Wilcoxon signed rank test, McNemar's chi-square test, Wald-Wolfowitz runs test, Mann-Whitney U test, Kolmogorov-Smirnov two-samples test, Kruskal-Wallis analysis of ranks, Spearman's R and Kendal's Tau), etc. Note a few texts say they are aimed at graduated level, partly because people from other fields only learn this material in graduated schools, as a result the texts have to set up basic probability and statistics (you have done it, stage 2 stuff) for them.

• 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.
• Hoel P.G. Introduction to Mathematical Statistics
• 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and Boes D.C. Introduction to the Theory of Statistics - As my lecturer Spiridon Penev have said, this text is a bit outdated but it contains useful exercise problems.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.