[Matematisk statistik] [Matematikcentrum] [Lunds tekniska högskola] [Lunds universitet]

Inference Theory, PhD Course

Institute/Department:
Mathematical Statistics, Mathematics Centre

Credits:
7.5 credits (10 ECTS credits)

Prerequisites:
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: March 16, 13.15-15.00 in MH227.
• There will be two two-hour lectures per week.
• The course time is 16/3-3/4 and 14/4-22/5.
• The exams will take place in the week 25/5-2/6.

Course Litterature:
The main course litterature is Van der Vaart's book (recommended buying), complemented with research papers. The other books are complementary reading.

• 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.
• List of papers with material relevant for the course (to be updated...).

Course content:
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.

Detailed schedule and course contents.

Examination:
The examination consist of two parts: 1) an oral exam at the end of the course, and 2) written and oral presentation of a home assignment. The questions at the oral exam will be picked from a list handed out in advance. The home assignment consist of reading a research paper (picked form a list provided by the lecturer) and presenting the material.

Lecturer spring 2009:
Dragi Anevski
dragi@maths.lth.se
phone: 046-222 96 11