Modulbeschreibung MA4472

# Modulbeschreibung

## MA4472: Multivariate Statistik

### Fakultät für Mathematik

Modulniveau:
Master
Sprache:
Englisch
Semesterdauer:
Einsemestrig
Häufigkeit:
Sommersemester
Credits*:
5
Gesamt-
stunden:

150
Eigenstudiums-
stunden:

105
Präsenz-
stunden:

45
* Die Zahl der Credits kann in Einzelfällen studiengangsspezifisch variieren. Es gilt der im Transcript of Records oder Leistungsnachweis ausgewiesene Wert.
Beschreibung der Studien-/Prüfungsleistungen:
The 60-minute written exam at the end of the course the students’ prove their abilities to derive selected multivariate densities by choosing and using appropriate characteristic functions and transformations. The students show, that they are able to define selected constructs correctly. They provide evidence, that they are able to assign the formulas correctly to the respective hypothesis tests, credible regions and parameter estimations and that they are able to apply them to solve numerical problems. They give problem specific interpretations of the results.
Wiederholungsmöglichkeit:
Im Folgesemester: Nein
Am Semesterende: Ja
(Empfohlene) Voraussetzungen:
MA1101 Linear Algebra 1, MA1102 Linear Algebra 2, MA1401 Introduction to Probability Theory, MA2402 Basic Statistics, MA4401 Applied Regression, multiple integration and working knowledge of the R package
Angestrebte Lernergebnisse:
At the end of this Master’s level course, students will be able to achieve the following outcomes: define the multivariate Normal and Wishart distributions, formally derive multivariate density functions using characteristic functions and transformations, stipulate hypothesis tests and multivariate credible regions, and perform multivariate regression.
Inhalt:
The focus of the course is on understanding the foundations and principles underlying the analysis of multivariate data of moderate dimensions. The need to handle large amounts of multivariate data and analyze for either summarization or prediction arises in most scientific fields, including genetics, genomics, psychology, sociology, finance, insurance and engineering. Sensible multivariate analysis and the ability to generalize to high-dimensional datasets relies on a firm foundation in the theory underlying multivariate testing and modelling. The course begins with definitions and properties of the multivariate Normal, spherical and Wishart distributions. It then moves to the Hotelling T² and Lambda statistics for measuring differences among mean vectors. It ends with coverage of multivariate analysis of variance (MANOVA), a special case of multivariate regresssion, also to be covered as time permits.
Lehr- und Lernmethode:
The module is offered as lectures with accompanying practice sessions. We encourage our students not only to develop individual learning strategies, but also to deepen their subject knowledge through independent practice. Traditional lecture-style teaching is supplemented with practical courses involving interactive group work and student-directed learning.
Medienformen:
blackboard, moodle
Literatur:
Fujikoshi, Y., Ulyanov, V.V. and Shimizu, R. (2010). Multivariate Statistics, Wiley.
Izenman, A.J. (2008). Modern Multivariate Statistical Techniques, Springer.
Johnson, R.A., Wichern, D.W. (2007). Applied Multivariate Statistical Analysis, Pearson.
Modulverantwortliche(r):
Ankerst, Donna; Prof. Ph.D.: ankerst@tum.de
Lehrveranstaltungen (Lehrform, SWS) Dozent(in):