MATH20802 - 2009/2010

 

Unit specification

Aims

To introduce estimation and hypothesis testing methods based on likelihood and other approaches.

Brief description

Statistical methodology is concerned with taking the numerical information contained in a sample (the data) and using it to make statements (or inferences) about the population from which the sample is drawn. In that the sample provides incomplete information about the entire population, there is inevitably some uncertainty relating to any inferences made. The methods developed in this course unit not only acknowledge this uncertainty but seek to model it in a meaningful way.

Intended learning outcomes

On successful completion of this unit students will:

• have an understanding of the underlying theory;
• be able to use these techniques on simple data sets.

Future topics requiring this course unit

Third and fourth level Statistics course units.

Syllabus

1. Parameter estimation: general framework and concepts, the likelihood function, maximum likelihood estimates and their properties, extensions to more than one sample and restricted estimation.
2. Hypothesis testing: elements of a statistical test, possible errors, the power function, the Neyman-Pearson Lemma, uniformly most powerful tests, generalised likelihood ratio tests.

Textbooks

• J.E. Freund, Mathematical Statistics with Applications, 7th edition, Pearson Prentice Hall 2004.
• W. Mendenhall, D.D. Wackerly and R.L. Scheaffer, Mathematical Statistics with Applications, PWS-Kent 1990.
• J.A. Rice, Mathematical Statistics and Data Analysis, 2nd edition, Duxbury Press 1995.

Learning and teaching processes

Two lectures and one examples class each week. In addition students are expected to do at least four hours private study each week on this course unit.

Assessment

Coursework; Weighting within unit 20%

2 hours end of semester examination; Weighting within unit 80%

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Arrangements