This course introduces students to the basic theory behind the development and assessment of statistical analysis techniques in the areas of point and interval estimation and hypothesis testing.

Topics include: Point estimation methods, including method of moments and maximum likelihood; Bias and variance; Mean-squared error and the Cramer-Rao inequality; Sufficiency, completeness and exponential families; the Rao-Blackwell theorem and uniformly minimum variance unbiased estimators; Bayesian estimation methods; Resampling estimation methods, including the jackknife and the bootstrap; Confidence interval construction methods, including likelihood-based intervals, inversion methods, intervals based on pivots and simple resampling-based percentile intervals; Highest posterior density and Bayesian credibility regions; Likelihood ratio tests and the Neymann- Pearson lemma; Power calculations and uniformly most powerful tests; Rank-based non-parametric tests, including the sign-test and Wilcoxon tests.

To achieve an understanding of and facility in:

• the notion of a parametric probability model, and point estimation of the parameters of these models.
• extend estimation procedures to include a measure of their accuracy and our confidence in them by examining the area of interval estimation.
• assessing the plausibility of pre-specified ideas about the parameters of the model by examining the area of hypothesis testing.
• non-parametric statistics, wherein estimation and analysis techniques are developed that are not heavily dependent on the specification of an underlying parametric model.

On completion of this course students should have an understanding of and be able to apply the techniques outlined in the course description.

A final examination (80%) and assignment (20%).

10 hours per week.

STAT2001 Introductory Mathematical Statistics

Please refer to Course Website