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MA40092: Classical statistical inference

[Page last updated: 22 May 2025]

Academic Year: 2025/26
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.


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.

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

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.

Course availability:

MA40092 is Optional on the following courses:

Department of Mathematical Sciences
  • 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 5)

Notes:

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