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MA40092: Classical statistical inference

[Page last updated: 23 October 2023]

Academic Year: 2023/24
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
  • Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20226
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.


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.

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.

Course availability:

MA40092 is Optional on the following courses:

Department of Economics
  • UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
  • UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
  • UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
  • UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
  • RSMA-AFM16 : Integrated PhD Statistical Applied Mathematics
  • TSMA-AFM17 : MRes Statistical Applied Mathematics
  • TSMA-AFM19 : MSc Mathematics with Data Science for Industry
  • TSMA-AWM19 : MSc Mathematics with Data Science for Industry
  • TSMA-AFM16 : MSc Statistical Applied Mathematics
  • USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
  • USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
  • USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
  • USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
  • USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
  • USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
  • USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
  • USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 3)
  • USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
  • USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
  • USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
  • USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

Notes:

  • This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
  • Courses and units are subject to change 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.
  • Find out more about these and other important University terms and conditions here.