# STATS 732 Introduction to Statistical Inference

Course year: 2011

Points: 15

Prereqs: 15 points from Stats 210 and 15 points from Maths 208, 250 or equivalent

Restrictions: STATS 310

Credit: Final exam 75% (100% if plussage applies), Assignments 15% (0% if plussage applies), Mid term test 10% (0% if plussage applies)

Textbooks: J.A. Rice, Mathematical Statistics and Data Analysis, 3rd edn (2005), Duxberry Press, available from the University Book Shop

For Advice: Arden Miller (Email: a.miller@auckland.ac.nz | extn: 85053)

Taught: First Semester City

Website: STATS 732 website

This course includes the material in STATS 310.
It is intended for postgraduate students who have not already passed STATS 310.

Students will attend lectures and tutorials for STATS 310. Additional material on Decision Theory and Bayesian Inference will be covered in STATS 732 workshops and tutorials.

Topics studied include:

Maximum likelihood estimation, likelihood and score functions, maximum likelihood estimates, Cramér-Rao lower bound, asymptotic optimality of maximum likelihood estimates, construction of confidence intervals. Multivariate Distributions, joint, marginal, and conditional distributions, vector random variables, variances and covariances, conditional means and variances, maximum likelihood estimates for multivariate parameters. Hypothesis testing, power and size of hypothesis tests, Neyman-Pearson lemma, link between hypothesis tests and confidence intervals. General linear models, least squares estimates, theory of estimation and testing for linear models Decision theory and Bayesian inference, decision rules, loss functions, risk functions, minimax rules, Bayes rules.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2011), is provided as a general guide only for students and is subject to alteration. All students enrolling at the University of Auckland must consult its official document, the University of Auckland Calendar, to ensure that they are aware of and comply with all regulations, requirements and policies.