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.

Final examination (80%)

Assignment (20%)

10 hours per week.

At least an average of 65% (or equivalent) in the final two years of an Australian undergraduate degree with at least two years of university level statistical and mathematical study including calculus and linear algebra, as well as mathematical statistics and linear regression theory.

Please refer to Course Website