Inference
4 points * First semester * Clayton * Prerequisites: MAT2020, MAS2011, MAS2032
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; 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. Transformations of random variables. Order statistics.
Assessment Examinations (1.5 hours): 80% * Assignments: 20%
Recommended texts
Bain L J and Engelhardt M Introduction to probability and mathematical statistics Duxbury, 1987
Hogg R V and Craig A T Introduction to mathematical statistics 4th edn, Collier Macmillan, 1978
Klimov G Probability and mathematical statistics MIR, 1986
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