Student Records
Programme & Unit Catalogues

## MA40092: Classical statistical inference

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 1
Assessment: EX 100%
Supplementary Assessment: MA40092 Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA20226
Description: Aims:
To develop a formal basis for methods of statistical inference including criteria for the comparison of procedures. To give an in depth description of the asymptotic theory of maximum likelihood methods and hypothesis testing.

Learning Outcomes:
On completing the course, students should be able to:
* calculate properties of estimates and tests;
* derive efficient estimates and tests for a broad range of problems, including applications to a variety of standard distributions;
* use the asymptotic theory for maximum likelihood estimators to derive approximate confidence intervals and tests.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F

Content:
Revision of standard distributions: Bernoulli, binomial, Poisson, exponential, gamma and normal, and their interrelationships. Sufficiency and Exponential families.
Point estimation: Bias and variance considerations. Rao-Blackwell theorem. Cramer-Rao lower bound and efficiency. Unbiased minimum variance estimators and a direct appreciation of efficiency through some examples.
Asymptotic theory for maximum likelihood estimators and its uses.
Hypothesis testing: Review of the Neyman-Pearson lemma and maximisation of power. Compound alternative hypotheses, uniformly most powerful tests. Compound null hypotheses, monotone likelihood ratio property. Generalised likelihood ratio tests, asymptotic theory, nuisance parameters. Examples relevant to other final year statistics units.
Programme availability:

#### MA40092 is Optional on the following programmes:

Programmes in Natural Sciences
• UXXX-AFB01 : BSc (hons) Natural Sciences (Full-time) - Year 3
• UXXX-AKB02 : BSc (hons) Natural Sciences with Industrial Placement (Full-time with Thick Sandwich Placement) - Year 4
• UXXX-AAB02 : BSc (hons) Natural Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• TSMA-AFM09 : MSc Mathematical Sciences (Full-time)
• TSMA-APM09 : MSc Mathematical Sciences (Part-time)
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time)
• TSMA-AWM14 : MSc Modern Applications of Mathematics (Full-time incorporating placement)
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time)

Notes:
* This unit catalogue is applicable for the 2013/4 academic year only. Students continuing their studies into 2014/15 and beyond should not assume that this unit will be available in future years in the format displayed here for 2013/14.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.