Statistics
ST414: Statistical Theory - Hypothesis Testing (5 ECTS)
NOT RUNNING IN ACADEMIC YEAR 2013-2014.
An advanced course on aspects of statistical theory with an emphasis on the principles and practice of hypothesis testing. Topics covered include hypotheses, test construction and critical regions, size and power, most powerful tests, Neyman-Pearson approach, likelihood methods, likelihood based tests, and an introduction to asymptotic results.
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 34 hours (24 Lecture hours, 10 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
find sufficient and minimal sufficient statistics for a general statistical model; formulate an hypothesis testing problem and evaluate a test procedure (critical region) in terms of size and power; use the Neyman-Pearson lemma to derive most powerful tests of simple hypotheses and extend these to uniformly most powerful tests for composite hypotheses; construct a likelihood function and find maximum likelihood estimates; use the likelihood ratio test for comparing nested models and for goodnees-of-fit testing; calculate the score function, observed and expected information form a specified likelihood function and use these for asymptotic parametric inference; test a single parameter using likelihood ratio, Wald and score tests.
Indicative Content
This course provides a more advanced view of statistical theory with an emphasis on hypothesis testing. The topics covered include:
- Sufficiency, minimal sufficiency, the exponential family. and the central role of likelihood.
- Hypothesis testing: Basic ideas, hypotheses, size, power function.
- Construction of tests: most powerful tests, Neyman-Pearson Lemma, uniformly most powerful tests, unbiased tests.
- Likelihood based tests: Likelihood ratio test, goodness-of-fit tests, Wald test, score test.
- Likelihood methods: maximum likelihood estimation, score function, observed and expected information, asymptotic results, profile likelihood.
Module Resources
- Statistical Inference (2nd Ed) by Casella & Berger, Duxbury.
- Introduction to the Theory of Statistics, Mood, Graybill & Boes, McGraw Hill
- Statistical Inference, Garthwaite, Jolliffe & Jones., Oxford
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