STAT8027 Statistical Inference

Offered By	School of Finance, Actuarial Studies & Appl Stats
Academic Career	Graduate Coursework
Course Subject	Statistics
Offered in	Second Semester, 2010 and Second Semester, 2011
Unit Value	6 units
Course Description	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.
Learning Outcomes	On completion of this course students should have an understanding of and be able to apply the techniques outlined in the course description.
Indicative Assessment	The assessment for this course is proposed to be made on the following basis: A final examination (80%) and 1 assignment (20%).
Workload	10 hours per week.
Course Classification(s)	AdvancedAdvanced courses are designed for students having reached 'first degree' level of assumed knowledge, which provide a deep understanding of contemporary issues; or 'second degree' and higher levels of knowledge; or for transition to research training programs.
Areas of Interest	Statistics
Eligibility	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.
Assumed Knowledge and Required Skills	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.
Prescribed Texts	See Course Outline: http://ecocomm.anu.edu.au/courses/outline/STAT8027.pdf
Preliminary Reading	See Course Outline: http://ecocomm.anu.edu.au/courses/outline/STAT8027.pdf
Indicative Reading List	See Course Outline: http://ecocomm.anu.edu.au/courses/outline/STAT8027.pdf
Programs	Master of Applied Statistics
Other Information	For further information please refer to http://ecocomm.anu.edu.au/courses/course.asp?code=STAT8027
Academic Contact	See http://ecocomm.anu.edu.au/courses/course.asp?code=STAT8027

The information published on the Study at ANU 2010 website applies to the 2010 academic year only. All information provided on this website replaces the information contained in the Study at ANU 2009 website.