**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, the maximum likelihood estimator, Bayes procedures, etc. Results and concepts from probability theory that need to be familiar: the law of large numbers and the central limit theorem; normal, exponential, gamma, binomial, poisson families of distributions etc. Furthermore, at least a passing familiarity with measure theory is extremely useful if not 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 the performance of statistical procedures from an asymptotic point of view.

**Some of the topics that will be treated**

Modes of stochastic convergence, multivariate normal distributions, delta method, consistency and asymptotic normality of Z- and M-estimators, Glivenko-Cantelli, rates of convergence of kernel estimators, minimax lower bounds, introduction to high-dimensional models

**Lecturers**

Bas Kleijn (UvA)

**Course website **

https://vu.amsterdamstatlab.nl/as/asymptotic-statistics-2021-2022.html

This contains the lecture notes, old exams, slides, weekly schedule, homework, etc.

- Docent: Bas Kleijn