Description

Any serious practitioner of statistics should have a good understanding of the principles of statistical inference. Such is the objective of this course, addressed to students in the MAS programme. As compared with Stat-6510, this course has the distinctive feature of adopting a practical approach through real life examples and exercises as the essential ingredients to present the material to
the students.

This course introduces the formal notion of parametric statistical model, the basis of data dimension reduction, and the essentials of parameter estimation and hypothesis testing.

Pre-requisites

A couple of basic courses in statistics, calculus, and familiarity with linear algebra and multiple integration.

Credit restriction

Stat-6509 is required for the MAS programme but cannot be used to satisfy the minimum course requirements of the M.Sc. in statistics programme.

Tentative course outline

1. Notions of probability and distribution theory.
2. Concepts of convergence and limiting distributions.
3. Sufficiency, completeness and ancillarity.
4. Point estimation.
5. Hypothesis testing.
6. Interval estimation.
7. Likelihood ratio test, Wald's test, and score test.
8. Large-sample inference and sample size determination.

Text and references

• An introduction to probability and statistical inference, 2nd ed, by GG Roussas. Academic Press, 2015. Chs. 4-12.
• Probability and statistical inference by N Mukhopadhyay. Marcel Dekker, Inc, 2000. Chs. 1, 5-9,11-12 (suggested text).
• Introduction to mathematical statistics, 8th ed, by RV Hoog, JW McKean and AT Craig. Pearson, 2015. Chs. 4-8.
• Principles of statistical inference by DR Cox. Cambridge University Press, 2006.
• Principles of applied statistics by RD Cox and CA Donnelly. Cambridge University Press, 2011.
• Applied statistics, principles and examples by DR Cox and EJ Snell, Chapman and Hall, 1981.
• A course in mathematical statistics, 2nd ed, by GG Roussas. Academic Press, 1997. Chs. 5-8, 11-15.