# Unit information: Statistical Asymptotics in 2015/16

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Unit name Statistical Asymptotics MATHM6010 10 M/7 Academic Year (weeks 1 - 52) Dr. Kovac Not open None None School of Mathematics Faculty of Science

## Description including Unit Aims

This unit has the twin aims of introducing students to asymptotic theory and developing their practical skills in using asymptotic approximations. Topics covered may include multivariate central limit theorem, the continuous mapping theorem, the delta method, likelihood asymptotics, Laplace's approximation and an introduction to Edgeworth expansions and saddlepoint density approximations. Prerequisites are a basic undergraduate knowledge of likelihood methods and univariate limit theorems, and a working knowledge of Taylor expansion methods and different modes of convergence.

Aims:

This unit has the twin aims of introducing students to asymptotic theory and developing their practical skills in using asymptotic approximations.

Only available as part of a 1+ 3 Statistics MRes + PhD programme.

## Intended Learning Outcomes

Students will be able to recall basic theory, discuss the principles underlying the methodology and compute appropriate asymptotic quantities for examples taken from each of the following topics:

• multivariate central limit theorem, the continuous mapping theorem, the delta method
• likelihood asymptotics (including asymptotic properties of MLEs);
• asymptotic normality of posterior distributions (parametric case);
• Laplace's approximation (univariate and multivariate);
• Edgeworth expansions and saddlepoint density approximations (via tilting)

## Teaching Information

Lectures and statistical computing laboratory work, exercises and tutorials.

## Assessment Information

Assessment will be by means of an extended project which has both a theoretical component (e.g. discussion of conditions for asymptotic normality in a particular set-up or derivation of a suitable approximation in particular examples) and a computational component (e.g. numerical implementation of a Laplace or saddlepoint approximation).

The assessment criteria for the project will be based on a suitably modified version of the current Mathematics Department Project Assessment form. The project will be marked by the member of staff in charge of the unit and by an independent second marker.

## Reading and References

• Applied Asymptotics, A R Brazzale, A C Davison, N Reid, CUP, 2007
• Asymptotic Statistics, A W van der Vaart, CUP, 1998