Probability, Distribution Theory and Inference
This information is for the 2012/13 session.
Dr Matteo Barigozzi, COL.7.11 and Dr Kostas Kalogeropoulos, COL.6.10
BSc Actuarial Science, BSc Accounting and Finance, BSc Business Mathematics and Statistics, BSc Econometrics and Mathematical Economics, BSc Mathematics and Economics, BSc Mathematics with Economics, BSc Econometrics and Mathematical Economics and MSc Econometrics and Mathematical Economics (Two Year Programme) and BSc Statistics with Finance. Available to General Course students and as an outside option.
MA100 Mathematical Methods and ST102 Elementary Statistical Theory. Students who have not taken these courses should contact Dr Kalogeropoulos.
The course covers the probability, distribution theory and statistical inference needed for third year courses in statistics and econometrics.
Michaelmas term (Dr Matteo Barigozzi): Events and their probabilities. Random variables. Discrete and continuous distributions. Moments, moment generating functions and cumulant generating functions. 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 (Dr K Kalogeropoulos): Functions of random variables. 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.
Lectures: 20 MT, 20 LT.
Seminars: 9 MT, 10 LT, 1 ST
Four term-time tests will measure students progress.
G C Casella & R L Berger, Statistical Inference (primary reading); R Bartoszyński & M Niewiadomska-Bugaj, Probability and Statistical Inference (stresses comprehension of concepts rather than mathematics, complimentary reading only); J Jacod & P Protter, Probability Essentials (for further reading, a more advanced text on probability, using measure theoretic concepts and tools, still very accessible).
Three-hour written examination in the ST.