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Mathematical Statistics

Course
2014-2015

Description
In statistics, we estimate/reconstruct objects from data. Given a noisy image for example, we try to reconstruct the underlying true image.

A first course in statistics typically deals with reconstruction of simple objects, such as the mean or the standard deviation. For many interesting applications, however, we want to assume as little as possible about the true underlying objects.

The most general theory in this direction is called nonparametric statistics. In nonparametric statistics, we reconstruct functions from data (an image can be viewed as a two-dimensional function, for example). The theory has been developed largely during the past years but remains a topic of active research with many challenging open problems. One of the nice features is that there is a notion of optimality and estimators (reconstruction methods) can be constructed that (nearly) achieve this optimal behaviour.

Course objectives
In the course we give a mathematical introduction to this field using the recent book “Introduction to nonparametric estimation” by A. Tsybakov and some unpublished lecture notes by Iain Johnstone as course material.

References
Tsybakov, A.: Introduction to nonparametric statistics. Springer, 2009.

Johnstone, I.: Gaussian estimation: Sequence and wavelet models. Lecture notes.
available from: http://statweb.stanford.edu/~imj/GE06-11-13.pdf

Prerequisites
None. An introduction to mathematical statistics, measure theory and functional analysis could be helpful but is not required.

Assessment method
Weekly homework assignments with math problems (1/3) and a final exam (2/3).

Registration
Via blackboard. Course material will be provided via
http://pub.math.leidenuniv.nl/~schmidthieberaj/mathstatFall2014.html

To be able to obtain a grade and the ECTS for the course, sign up for the (re-)exam in uSis ten calendar days before the actual (re-)exam will take place. Note, the student is expected to participate actively in all activities of the program and therefore uses and registers for the first exam opportunity.

Exchange and Study Abroad students, please see the Prospective students website for information on how to apply.

Contact information