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This entry is from Winter semester 2022/23 and might be obsolete. No current equivalent could be found.

High-dimensional Statistics
(dt. Hochdimensionale Statistik)

Level, degree of commitment Specialization module, compulsory elective module
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics.
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. Hajo Holzmann

Contents

  • Linear regression model and least squares
  • Penalization with lasso, BIC,
  • sparsity
  • Convergence rates with respect to the mean squared prediction error and the mean squared error
  • lower bounds
  • variable selection
  • elements of estimating large matrices, such as covariance matrices, principal component analysis


Qualification Goals

The students shall

  • acquire theoretical knowledge of current research in the field of high-dimensional statistics,
  • get to know important algorithms and their functionality in the programming language R,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstraction, proof methods),
  • improve their oral communication skills in the recitation class by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Mathematical Statistics.


Applicability

Module imported from M.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Data Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics

When studying B.Sc. Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module is assigned to Applied Mathematics. Further information on eligibility can be found in the description of the study area.


Recommended Reading

  • Bühlmann, P., van de Geer, S. „Statistics for High-Dimensional Data“, Springer 2011



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2022/23. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.