Course category:2nd year
Please note that this module can be taken by some combined degree 3rd year students with the title Statistical Theory 1 and the module code 0590015
The aim of the module is to extend your knowledge of statistical theory and its applications to introduce you to some of the basic methods of statistical inference and estimation, which are needed in data analysis. The aim will be achieved through a mixture of theory and practice.
At the end of the module you should be able to...
Background. Probability, random variables and probability distributions, moment generating function and transformations of random variable.
Joint distributions. Discrete and continuous random variables, conditional distributions, expectation and variance, conditional expectations and transformations of random variables. Bivariate normal distribution, chi-square, t- and F-distributions.
Limit theorems. Modes of convergence (in distribution, in probability, almost surely), Central Limit Theorem, Weak Law of Large Numbers, Strong Law of Large Numbers.
Estimation of parameters. Point estimation: generalities. Unbiased and consistent estimators, MSE distance, efficient and sufficient estimators, Factorisation Theorem, the method of moments, the method of maximum likelihood, Cramer-Rao bound, efficiency of ML estimators under Gaussianity.
Students should obtain copies of the following tables:
One and a half hour closed examination in week 1 Spring Term.
Introduction to distributions arising in inference from normally distributed samples (and some others). Central limit theorem. Sample mean and variance.
Please check prerequisites carefully before asking to take this module as an elective. In choosing this module as an elective it will be assumed that you are familiar with all the material taught in the first year courses Calculus and Core Algebra, or are willing to learn the material if necessary.
Department of Mathematics, University of York, Heslington, York, UK. YO10 5DD