**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*Introduction to the Theory of Statistics*- As my lecturer Spiridon Penev have said, this text is a bit outdated but it contains useful exercise problems.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.

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