# ADVANCED MATHEMATICAL STATISTICS - 2022/3

Module code: MATM055

Module Overview

MATM055 builds on the material on statistical inference, hypothesis testing and interval estimation encountered in modules at lower levels. Topics in point estimation encompass: comparison of estimators; the concept of sufficiency; identification of minimum variance unbiased estimators. Fundamental methods of estimation are covered. The construction of exact and approximate confidence intervals using pivots is developed. Aspects of hypothesis testing include the Neyman-Pearson lemma, uniformly most powerful tests and likelihood ratio tests.

Module provider

Mathematics

WOLF Martin (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 7

JACs code: G120

Module cap (Maximum number of students): N/A

Independent Learning Hours: 112

Lecture Hours: 33

Practical/Performance Hours: 5

Module Availability

Semester 1

Prerequisites / Co-requisites

MAT2013

Module content

Indicative content includes:

Point Estimation:

• Comparison of estimators and the Cramer-Rao lower bound.

• Sufficient statistics and complete sufficient statistics.

• Exponential families of distributions

Methods of Estimation:

• Method of moments

• Method of maximum likelihood estimators and their limiting distributions

• Method of least squares

Interval Estimation:

• Confidence intervals

• Pivots and exact confidence intervals

• Asymptotic pivots and approximate confidence intervals

• Connection between confidence intervals and hypothesis tests

• Tests and confidence intervals for two sample problems

Hypothesis Testing:

• Type I and type II errors

• Neyman-Pearson lemma

• Generalised likelihood ratio tests

• Wilks’ theorem

Assessment pattern

Assessment type Unit of assessment Weighting
Examination Examination 80
School-timetabled exam/test Class test 20

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

• Analytical ability by solution of unseen problems in the test and exam.

• Subject knowledge through the recall of key definitions, theorems and their proofs.

Thus, the summative assessment for this module consists of:

• One two hour examination (students have the choice of three questions out of four to contribute to exam mark) at the end of the semester; weighted at 80% of the module mark.

• One class test; weighted at 20% of the module mark.

Formative assessment and feedback

Students receive written feedback via a number of marked unassessed coursework assignments over an 11 week period.

Module aims

• Provide students with a detailed understanding of the principles of efficient estimation and hypothesis testing.
• Equip students with skills to be able to determine the quality of an estimator or test procedure.

Learning outcomes

Attributes Developed
001 Demonstrate an advanced understanding of principles and theory of estimation and hypothesis testing. CKT
002 Assess the properties of an estimator or test procedure using a number of criteria. CKP
003 Construct estimators and test procedures based. CKP

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A good grounding in statistical inference.

• Experience in problem solving for the cognitive skills.

The learning and teaching methods include:

• 3 x 1 hour lectures per week x 11 weeks.

• 5 x 1 hour practice classes, fortnightly.

• Several pieces of unassessed coursework to give students experience of using techniques introduced in the module and to receive formative feedback.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MATM055

Other information

N/A

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 1 Compulsory A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2022/3 academic year.