» Stipendiaten » Alexander Meister » Nonparametric Statistics

Nonparametric Statistics

dates: Monday, 10:00 -- 11:30,    room: Helmholtzstr. 18/ 120,    type: lecture
             Thursday, 8:15 -- 9:45,    room: Helmholtzstr. 18/ 220,    type: lecture/exercise (changes fortnightly)

The lectures commence on Monday, 15 October 2007. The first hour of exercises takes place on Thursday, 25 October 2007.

scope: 3 hours of lectures + 1 hour of exercises per week.

prerequisites: Good knowledge of undergraduate mathematics (analysis, linear algebra, probability theory) is required. Further knowledge acquired by lectures on statistics and functional analysis is advantageous but not necessary. The lectures are held in English so that master students are also able to participate. We strongly recommend the lectures to any student who thinks of specialising in the fields of mathematical statistics, data-analysis, econometrics, biometrics, medical statistics, information theory etc.. But, of course, students from other branches are welcome, too.

contents: First, we will introduce standard models in nonparametric statistics such as density estimation and estimation of a regression function along with their applications. Unlike in parametric approaches to statistics, we do not assume shape conditions which determines the function to be estimated up to finitely many real-valued parameters. Therefore, the goal of nonparametric methods is covering much more general situations compared to classical statistical techniques.

We will derive famous estimation nonparametric procedures such as kernel methods and orthogonal series estimators. The underlying asymptotic theory is studied: We will establish general consistency results and show that those estimators achieve optimal rates of convergence under smoothness conditions. Adaptive selection of the smoothing parameters is discussed.

Subject to enough time, topics on support estimation, nonparametric testing, mode estimation, density deconvolution may be included in the lectures.

literature:

• Devroye, L. & Györfi, L., Nonparametric density estimation: the L1 view, 1985, John Wiley & Sons
• Silverman, B.W., Density estimation for statistics and data analysis, 1986, Chapman & Hall
• LeCam, L.M. & Yang, G.L., Asymptotics in statistics: some basic concepts, 1990, Springer, Heidelberg
• Härdle, W., Applied nonparametric regression, 1991, Cambridge University Press

etc.

exams: Any student who is interested in doing an exam on the lectures shall contact the lecturer for further details by the end of the lectures. The exam will be obligatory for master students who want to acquire some credit points, in addition to the requirements of the "Übungsschein", please see below.

exercises: The students have to prepare the exercises in advance. At the beginning of any hour of exercises, each student ticks off those exercises which he has solved. The student may be chosen to present his solution at the blackboard for each exercise that he has ticked off.

In order to receive an "Übungsschein" (= certificate saying that the student has successfully taken part in the exercises) at the end of WS 07/08,

• the student must have attended the lectures and exercises regularly;
• and he must have ticked off at least 75% of the exercises, overall;
• and he must have orally presented his correct (!) solutions of at least three exercises - up to minor mistakes.

Any sheet of exercises (pdf-files) is published one week before it is due. The sheets can be downloaded below:


1st sheet of exercises (for 25 Oct 2007)

2nd sheet of exercises (for 15 Nov 2007)

3rd sheet of exercises (for 29 Nov 2007)

4th sheet of exercises (for 13 Dec 2007)

5th sheet of exercises (for 10 Jan 2008)

6th sheet of exercises (for 24 Jan 2008)