619-320 Inference

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Objectives:

Students completing this subject should:

Comprehend:

• the concepts of estimation and hypothesis testing; and the relation between confidence regions and hypothesis tests;

• the existence of a range of different approaches to statistical inference.

Have developed the skills:

• to use a range of methods of estimation, in particular maximum likelihood estimation;

• to assess the relative performance of estimators;

• to assess the relative performance of statistical tests.

Appreciate:

• the theory and methodology of a range of different approaches to statistical inference, including distribution-free methods, robust methods, Bayesian methods and resampling methods.

Content:

Estimation; consistency; bias; information-function; Cramer-Rao lower bound; efficiency; sufficiency; Blackwell-Rao theorem; maximum likelihood estimators and their asymptotic properties; comparison of methods of estimation; hypothesis testing; size and power of tests; Neyman-Pearson lemma; uniformly and locally most powerful tests; similar region tests; likelihood ratio tests; confidence regions; distribution-free and Bayesian methods; comparison with classical methods; jack-knife and bootstrap techniques; robust estimation.

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