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# ECON2006 Statistical Theory 2

## Module Overview

To cover the parts of statistical distribution theory and statistical inference essential to a full understanding of econometrics and applied statistics. It develops ideas presented in ECON1007 and ECON1011 and applies mathematical techniques from ECON1008

### Aims and Objectives

#### Module Aims

This module aims to cover the parts of statistical distribution theory and statistical inference essential to a full understanding of econometrics and applied statistics. It develops ideas presented in ECON1007 and ECON1011 and applies mathematical techniques from ECON1008.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Relate the theoretical results in the module to one another, and apply them in problem solving
• Demonstrate knowledge and understanding of some basic ideas on which further modules build

### Syllabus

The module covers the following topics: * Distribution Theory: Multivariate distributions: marginal and conditional distributions, multivariate normal. Relations between normal, chi-square, F, t and Cauchy distributions. Asymptotic theory: probability limits and the central limit theorem. * Inference: Estimation: Cramer-Rao inequality and Rao-Blackwell theorem. Maximum likelihood. Hypothesis testing: Neyman-Pearson Lemma and Likelihood Ratio Tests.

#### Special Features

With ECON1011 and ECON2007 the module enables exemption to be gained from the Institute of Actuaries Core Technical examination in statistics. This constrains the amount of choice available on the examination paper

### Learning and Teaching

TypeHours
Independent Study122
Teaching28
Total study time150

#### Resources & Reading list

Mathematical Statistics with Applicationsi.

### Assessment

#### Assessment Strategy

The module uses mathematical techniques (mainly integration, differentiation and limits) to establish relationships between distributions, and the principles of classical statistical inference. A variety of distributions (Binomial, Poissson, negative Binomial, exponential, normal, gamma…) can be used to exemplify and illustrate both the distribution theory and the inference. The formative assessment consists of up to 10 exercises to give the students practice in applying techniques while familiarising them with the results. These do not form par of the summative assessment as to is very difficult to set progressive problem exercises without giving the students incentives to simply copy from one another. The examination assesses their familiarity with the techniques and results, and the facility with which the candidates can employ and present these.

#### Summative

MethodPercentage contribution
Coursework 10%
Exam  (2 hours) 90%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

### Linked modules

#### Pre-requisites

To study this module, you will need to have studied the following module(s):

CodeModule
ECON1011Quantitative Modelling in Economics
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