In Asymptotic Statistics we study the asymptotic behaviour of (aspects of) statistical procedures. Here “asymptotic” means that we study limiting behaviour as the number of observations tends to infinity. A first important reason for doing this is that in many cases it is very hard, if not impossible to derive for instance exact distributions of test statistics for fixed sample sizes. Asymptotic results are often easier to obtain. These can then be used to construct tests, or confidence regions that *approximately* have the correct uncertainty level. Similarly, determining estimators or other procedures that are optimal in a specific sense, for instance in the sense of minimal mean squared error or variance, is often not possible if the number of observations is fixed. Using asymptotic results is it however in many cases possible to exhibit procedures that are *asymptotically* optimal.

In this course we begin by treating the mathematical machinery from probability theory that is necessary to formulate and prove the statements of asymptotic statistics. Important are the various notions of stochastic convergence and their relations, the law of large numbers and the central limit theorem (which the students are assumed to know), the multivariate normal distribution, and the so-called delta method. We will use these tools to study the asymptotic behaviour of statistical procedures.

It is assumed that students have at least successfully completed introductory courses on probability theory and statistics and courses on linear algebra and multivariate calculus. It is highly recommended to follow a course on measure theoretic probability.

### Announcements

- none at this time

### Course information

- Lecturer: Harry van Zanten
- TA: Paul Dobson
- 2 hours of lecture + 1 hour exercise class every week
- Lecture notes: can be downloaded here.
- Recommended literature:
*Asymptotic Statistics*, by A.W. van der Vaart, Cambridge University Press. - Exams: midterm exam (40%) + final exam (60%). You need at least a 5.0 for the final exam in order to pass. Retake is a single exam (100%).

### Slides

### What we have done so far

Lecture | Date | Topic | Material | Exercises | Remarks |

1 | 11/9 | introduction, convergence | slides+notes Sec. 1.1 up to and including Theorem 1.7 | 1.1, 1.2, 1.3, 1.4, 1.10, 1.15 | |

2 | 18/9 |