Nonparametric Inference

Institute/Department:
Mathematical Statistics, Mathematics Centre

Credits:
7.5 credits (7.5 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 is Monday January 21, 13:15-15:00 in MH:R.
• There will be two two-hour lectures per week, on Mondays, 13:15-15:00 and on Wednesdays 15:15-17:00, (almost) all in MH:309A. The time schedule and room numbers can be found here.
• The course will run over the first half of the spring semester.

Lecturer:

Dragi Anevski, dragi@maths.lth.se, room MH505.

Course Litterature:
The main course literature 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. 

We have electronic access to Van der Vaart's book and Billingsley's, at Van der Vaart and Billingsley (this is the second edition from 2008). 

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. An overview of the curse content can be found here.

Examination:
The examination consist of a presentation of a published research paper or of chapters in research monograph such as Billingley's or Van der Vaart and Wellner's books, at the end of the course.

• A list (preliminary) of papers/chapters to choose from can be found here.