Multivariate Analysis

Lecturer: Markus Pauly and Sarah Friedrich

Exercises: Burim Ramosaj and Thilo Welz

General Information

 Language English Lectures 4 h Exercises 2 h

Time and Venue

 Lectures Monday, 12 - 2 p.m., He 18, 120Thursday, 8 - 10 a.m., He 18, 120 Exercise Tuesday, 4 - 6 p.m., He 22, E.04

Exam:

Final Exam: in Heho 18, Room 120 on Monday, July 16, 2018 from 11.30am - 02.00pm

Retake Exam: tba.

General Informations:

 Prerequisites: Analysis I-II; Linear Algebra I-II; Stochastics I; Elementary Probability and Statistics Exam: In order to be admitted to the exam, students must have achieved at least 40% of all exercise points.

Aims:

Multivariate analysis is in principle a collection of methods designed to elicit information from multivariate data and to answer different statistical questions of interest.
In particular, students will

• get to know different (parametric and nonparametric) statistical models which are most popular for describing multivariate data in practice and will
• be familiar with the corresponding inference procedures as hypothesis tests (e.g. Wilk's Lambda) and confidence ellipsoids,
• learn about specific classification and grouping methods and their properties and
• be able to apply their knowledge to real data.
• Finally, if there is enough time left, we will also treat modern statistical learning techniques for (multivariate) classification and prediction problems.

Contents:

• Data visualization. How to present multivariate data?
• Hypothesis construction and testing; e.g. likelihood-ratio-tests and nonparametric tests
• Confidence ellipsoids
• Dimension reduction or structural simplification and their limitations
• Investigation of dependence among variables
• Bootstrap for multivariate data
• Classification and Prediction

Exercise Sheets:

The exercise sheets are on Moodle.