134 Advanced statistics: statistical inference (half unit)

Prerequisite

If taken as part of a BSc Degree, 04A Statistics 1 and 04B Statistics 2 as a
prerequisite. A high level of competence in mathematics is also assumed.

This unit must be taken at the same time as, or after unit 133 Advanced statistics:
distribution theory.
Aims and objectives
The aim of this half unit is to provide a thorough theoretical grounding in statistical
inference. The unit teaches fundamental material that is required for specialised
units in statistics, actuarial science and econometrics.
Learning outcomes
After successfully completing this half unit students will:
? Be familiar with the principles of data reduction.
? Understand how the quality of estimators is judged.
? Be able to choose appropriate methods of inference to tackle real problems.
Syllabus
Data reduction; Sufficiency, minimal sufficiency. Likelihood.
Point estimation; Bias, consistency, mean square error. Central limit theorem. Rao-Blackwell
theorem. Minimum variance unbiased estimates, Cramer-Rao bound.
Properties of maximum likelihood estimates.
Interval estimation; Pivotal quantities. Size and coverage probability.
Hypothesis testing; Likelihood ratio test. Most powerful tests. Neyman-Pearson
lemma.
Essential reading
Casella, G. and R.L. Berger Statistical Inference. (Duxbury, 2002) second edition
[ISBN 0534243126].
Hogg, R. and E. Tanis Probability and Statistical Inference. (Prentice-Hall, 2001)
sixth edition [ISBN 0130272949].

Assessment
This half unit is assessed by a two hour unseen written examination.

All information in this document is subject to confirmation in the Programme Regulations for
degrees and diplomas in Economics, Management, Finance and the Social Sciences that are
reviewed annually. Notice is also given in the Regulations of any units which are being phased
out and students are advised to check unit availability.