Objectives: 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.

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

The assessment for this course is proposed to be made on the following basis: A final examination (80%) and 1 assignment (20%).

10 hours per week.

A basic knowledge of introductory mathematics and statistics will be assumed. In particular, we shall assume that students are familiar with the following concepts:

• Maximisation and minimisation of functions;
• Taylor-series expansions;
• Basic probability and random variables;
• Joint and marginal distributions and independence;
• Moments of random variables and moment generating functions;
• The change of variable formula for probability densities; and,
• Basic conditional distributions and conditional expectations.

For further information please refer to http://ecocomm.anu.edu.au/courses/course.asp?code=STAT3013