Mathematical Statistics, Mathematics Centre
7.5 credits (7.5 ECTS credits)
Second courses in probability theory and inference theory, corresponding to MASC01 (MAS203) and MASC02 (MAS207). Courses in measure theory, corresponding to MATP14, and topology, corresponding to MATM16, are recommended but not strictly necessary.
Time and place:
- Introductory lecture is Tuesday January 17, 10:15-12:00 in MH227
- There will be two two-hour lectures per week, on Tuesdays, 10:15-12:00 in MH227 and Thursdays 10:15-12:00 in MH227.
- The course will run over the first half of the spring semester.
The main course litterature is Van der Vaart's book (recommended buying), complemented with research papers. The other books are complementary reading. All three books are excellent reference literature.
- Van der Vaart (1998), "Asymptotic Statistics", Cambridge University Press. (main source).
- Van der Vaart and Wellner (1996), "Weak convergence and empirical processes", Springer.
- Billingsley (1968), "Convergence of Probability Measures", Wiley.
The goal of the course is to provide a set of tools and results used in modern inference theory. Many of the key concepts are applied to modern survival analysis, density and regression function estimation, spectral density estimation, and thus the course can also be seen as an introduction to these areas. We will also cover some nonstandard topics, such as empirical process theory for stationary data, and estimation of the spectral measure of stationary processes. An overview of the curse content can be found here.
The examination consist of a presentation of a published research paper, at the end of the course.