|Owning Department/School:||Department of Mathematical Sciences|
|Level:||Masters UG & PG (FHEQ level 7)|
|Supplementary Assessment:||MA40092 Mandatory Extra Work (where allowed by programme regulations)|
|Requisites:||Before taking this unit you must take MA20226|
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.
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.
Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F
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.
MA40092 is Optional on the following programmes:Programmes in Natural Sciences