Prerequisites

It is assumed that participants in the course have, at the least, some knowledge of the basic concepts in statistics: estimation, testing and confidence sets; the definitions of moment estimators and the maximum likelihood estimator; the law of large numbers and the central limit theorem; normal, exponential, gamma, binomial, poisson families of distributions etc. For examples, see the very accessible text:

F. Bijma, M. Jonker, A. van der Vaart, ‘Inleiding in de Statistiek’, Epsilon Uitgaven, Utrecht, 2016.

Furthermore, at least a passing familiarity with measure theory is indispensable at the beginning of the course: concepts like sigma-algebras, measurable functions, measures, sigma-additivity, integration, monotone limits, etc, should not be wholly unknown. For those participants who feel under-equipped measure-theoretically, the (simultaneous) course in Measure Theoretic Probability is highly recommended.

Aim of the course

Learn to study statistical procedures from an asymptotic point of view.

The course starts with a review of various concepts of stochastic convergence (e.g. convergence in probability or in distribution) and properties of the multivariate normal distribution. Then the asymptotic properties of various statistical procedures are studied, including Chi-square tests, Moment estimators, M-estimators (including MLE) and Bayesian procedures. The examples are chosen according to importance in practical applications, and the theory is motivated by practical relevance, but the subjects are presented in theorem-proof form.