Dr Miltiadis Mavrakakis-Vassilakis

This course is compulsory on the BSc in Actuarial Science and BSc in Financial Mathematics and Statistics. This course is available on the BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

Students must have completed Elementary Statistical Theory (ST102) and Mathematical Methods (MA100).

Students who have not taken these courses should contact Dr Mavrakakis.

The course covers the probability, distribution theory and statistical inference needed for third year courses in statistics and econometrics.

Michaelmas term: Events and their probabilities. Random variables. Discrete and continuous distributions. Moments, moment generating functions and cumulant generating functions. Functions of random variables. Monte Carlo Simulation using R. Joint distributions and joint moments. Marginal and conditional densities. Independence, covariance and correlation. Sums of random variables and compounding. Multinomial and bivariate normal distributions. Law of large numbers and central limit theorem.

Lent term: Sampling distributions. Criteria of estimation: consistency, unbiasedness, efficiency, minimum variance. Sufficiency. Maximum likelihood estimation. Confidence intervals. Tests of simple hypotheses. Likelihood ratio tests. Wald tests, score tests. Introduction to linear regressions and least squares estimator.

This course will be delivered through a combination of classes and lectures totalling a minimum of 60 hours across Michaelmas Term and Lent Term. This year, some of this teaching may be delivered through a combination of virtual classes and flipped-lectures delivered as short online videos. This course includes reading weeks in Week 6 of Michaelmas Term and Lent Term.

Students will be expected to produce 4 pieces of coursework in the MT and LT.

These are exam-style class tests.

M C Mavrakakis & J Penzer, Probability and Statistical Inference: From Basic Principles to Advanced Models (primary reading)

G C Casella & R L Berger, Statistical Inference (very useful as a reference)

Exam (50%, duration: 2 hours) in the January exam period.
Exam (50%, duration: 2 hours) in the summer exam period.

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.