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Semester 1

Theory of Statistical Inference (MATH10028)

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Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.

Course Summary

In this course we will develop mathematical aspects of statistical inference. The theory covered provides a greater understanding of the fundamental properties of popular statistical techniques and provides a framework for deriving procedures in more complex situations.

Course Description

Topics to be covered include:1. Parametric families and likelihood.2. Statistics, Sufficiency and Minimal Sufficiency.3. Estimation, Unbiasedness, Efficiency, MVUE, Rao--Blackwell Theorem, Cramer--Rao Lower Bound.4. Hypothesis testing, Neyman--Pearson Lemma.5. Confidence Intervals, Pivots6. Decision theory and admissibility of estimators.7. Shrinkage/James Stein estimators.8. Selected topics in modern statistics.

Assessment Information

Written Exam 95%, Coursework 5%, Practical Exam 0%

Additional Assessment Information

Coursework 5%, Examination 95%

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