Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-62-12-M-7

Nonparametric Statistics (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-62-12-M-7 Nonparametric Statistics 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V MAT-62-12-K-7
Nonparametric Statistics
P 56 h 214 h - - PL1 9.0 irreg.
  • About [MAT-62-12-K-7]: Title: "Nonparametric Statistics"; Presence-Time: 56 h; Self-Study: 214 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86320 ("Nonparametric Statistics")

Evaluation of grades

The grade of the module examination is also the module grade.


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.

Competencies / intended learning achievements

Upon successful completion of the module, the students have gained a good overview of modern statistic methods which can be applied without restrictive assumptions of the model but require a great amount of data and high computing time. They have also gained basic knowledge of the theory and algorithms of nonparametric statistics. They can critically analyze the possibilities and limitations of the use of data-driven classification, pattern recognition, function estimation and predictions.

The students have gained a precise and independent handling of terms, propositions and methods of the lecture. They understand the proofs presented in the lecture and are able to reproduce and explain them.

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.

References to Module / Module Number [MAT-62-12-M-7]

Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-65-MPOOL-7] Specialisation Image Processing and Data Analysis (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)