Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-62-12-K-7

Nonparametric Statistics (4V, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
4 V Lecture 9.0 CP 56 h 214 h
(4V) 9.0 CP 56 h 214 h

Basedata

SWS 4V
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Additional informations
Livecycle-State [NORM] Active

Contents

Smoothing Methods for Estimating Functions:
  • Smoothing methods for estimating functions (kernel estimator, local polynomial estimator, next-neighbour-estimator, smoothing splines) and their asymptotic analysis,
  • Application in regression and image analysis,
  • Data controlled choice of smoothing parameters with cross-validation,
  • Spectral decomposition and spectral estimators for stationary time series.

Nonparametric Regression and Classification:

  • Analysis of regression in higher dimensions on the basis of Boosting,
  • General sieve estimators for functions and their asymptotic analysis,
  • Trees of regression and classification, neuronal networks, expansion of orthogonal series and wavelets for example,
  • Applications for estimating functions and solving classification problems with high dimensional causal variables.

Literature

  • L. Györfy, M. Kohler, A. Krzyzak, H. Walk: A Distribution-Free Theory of Nonparametric Regressions,
  • W. Härdle: Applied Nonparametric Regression,
  • B. Silverman: Density Estimation for Statistics and Data Analysis.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-62-12-K-7]

Module Name Context
[MAT-62-12-M-7] Nonparametric Statistics P: Obligatory 4V, 9.0 LP