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Courses in Mathematics and Statistics Level 1 Modules Level 2 Modules Level 3 Modules Level 4 Modules Level 5 Modules Honours timetable 2011/2012 Sem. 1 2011/2012 Sem. 2 2012/2013 Sem. 1 & Sem. 2 2013/2014 Sem. 1 & Sem. 2

MT4606 STATISTICAL INFERENCE Aims - To show how the methods of estimation and hypothesis testing met in MT2004 and MT3606 can be justified and derived. - To extend those methods to a wider variety of situations. - To show how different point estimators can be compared. Objectives By the end of the course students are expected to - be familiar with the distributions listed in the syllabus. - understand the main problems in comparing the usefulness of two estimators. - identify sufficient statistics and appreciate why they are important. - derive bounds on variances provided by the Cramér-Rao inequality. - derive maximum likelihood estimators of one and two dimensional parameters and establish their major properties. - apply the Neyman-Pearson lemma for testing simple hypotheses. - determine and use the generalised likelihood ratio statistic when testing composite hypotheses. - appreciate the relationship between frequentist confidence sets and tests of hypotheses. Syllabus - Distribution theory: Multinomial and negative binomial distributions. - Point estimation: Mean square error. Unbiasedness. Sufficiency. The efficient score. Fisher Information. - The Cramér-Rao lower bound. Exponential families. Attainment of the Cramér-Rao lower bound. - Multi-dimensional Cramér-Rao inequality. Maximum likelihood estimation. Consistency and asymptotic efficiency. - Hypothesis testing: Neyman-Pearson lemma. Uniformly most powerful tests. Likelihood ratio tests. - Confidence sets: Pivotal quantities. Textbooks Introduction to the Theory of statistics: A M Mood, F A Graybill & D C Boes, McGraw Hill; Probability and Statistics: M H DeGroot, Addison-Wesley; Statistical Inference: G Casella & R L Berger, Brooks/Cole; Statistical Inference: S D Silvey, Chapman & Hall; Statistical Theory: B W Lindgren, Collier MacMillan. Assessment 2 Hour Examination = 100% Prerequisites MT3606 Antirequisites MT5701 Availability Academic year 2013/14 in semester 2 at 12 Lecturer Dr I B J Goudie Click here to see the University Course Catalogue entry. Revised: PMH (April 2012)