MAT3232

Inference

Coordinator: Dr Robert Griffiths

4 points
* Two 1-hour lectures per week
* Second semester
* Clayton
* Prerequisites: MAT2061, MAS2032 or MAT2222
* Prohibitions: MAS3131

Objectives On the completion of this subject students will be able to understand transformation theory to find the density functions of derived random variables; derive the density function of order statistics; discuss and understand the broad principles of statistical inference as a scientific procedure; discuss the broad criteria for estimation, in particular the concepts of unbiasedness and efficiency; know the detailed statistical aspects of estimation theory deriving from the above criteria, including in particular the concepts of sufficient statistics and maximum likelihood estimation; discuss the value of confidence intervals for parameters (as well as estimates), and to develop methods for finding these; apply the jackknife and bootstrap to obtain standard errors of estimators; discuss the problem of statistical hypothesis testing and to consider various approaches to this deriving statistical tests; know the approach to hypothesis testing deriving from the concept of most powerful tests, leading to the standard, and various new, testing procedures; discuss difficulties with this approach to hypothesis testing and to consider alternative approaches.

Synopsis Principles of estimation: efficiency, the Cramer-Rao inequality, sufficiency, maximum likelihood estimates and their optimality properties. Hypothesis testing. Most powerful tests, the Neyman-Pearson lemma. The [lambda] ratio procedure and derivation of statistical tests. Resampling procedures: the jackknife, the bootstrap. Transformations of random variables. Order statistics.

Assessment Examination (2 hours): 80%
* Assignments: 20%

Recommended texts

Bain L J and Engelhardt M Introduction to probability and mathematical statistics Duxbury, 1987