Modulbeschreibung MA5441

# Modulbeschreibung

## MA5441: Fundamentals of Mathematical Statistics

### Fakultät für Mathematik

Modulniveau:
Master
Sprache:
Englisch
Semesterdauer:
Einsemestrig
Häufigkeit:
Unregelmäßig
Credits*:
9
Gesamt-
stunden:

270
Eigenstudiums-
stunden:

180
Präsenz-
stunden:

90
* 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 module examination is based on a written exam with video surveillance (90 minutes). The exam tests that students have gained deeper knowledge of definitions and main mathematical results relevant to core principles of mathematical statistics, including likelihood methods and asymptotic distribution theory. Furthermore, the students demonstrate that they know how to apply general statistical methods for parameter estimation and testing in the context of specific models.
Wiederholungsmöglichkeit:
Im Folgesemester: keine Angabe
Am Semesterende: Ja
(Empfohlene) Voraussetzungen:
MA1401 Introduction to Probability Theory (MA2409 Probability Theory), MA2402 Basic Statistics
Angestrebte Lernergebnisse:
Upon successful completion of this module, students understand general principles and theory of statistical inference, such as maximum likelihood. They are able to derive asymptotic properties of estimators and tests, and they are able to apply the statistical methodology in practice.
Inhalt:
This course introduces general principles and methods of statistical inference and studies their theoretical properties. We will discuss decision-theoretic underpinnings, and introduce concepts such as likelihood-based inference, Bayesian inference, and minimax estimation. We will develop asymptotic theory for statistics calculated from large samples. This theory will be applied, in particular, in a detailed study of maximum likelihood techniques.
Lehr- und Lernmethode:
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.
Medienformen:
blackboard, slides
Literatur:
T.S. Ferguson. A Course in Large Sample Theory, Chapman and Hall, 1996.
E.L. Lehmann and G. Casella. Theory of Point Estimation, Second Edition. Springer, 1998.
Aad van der Vaart. Asymptotic Statistics, Cambridge University Press, 1998.
Modulverantwortliche(r):
keine Angabe: keine Angabe
Lehrveranstaltungen (Lehrform, SWS) Dozent(in):

0000001985 Exercises for Fundamentals of Mathematical Statistics [MA5441] (2SWS UE, WS 2020/21)
Drton M, Grosdos Koutsoumpelias A, Wu J

0000004689 Fundamentals of Mathematical Statistics [MA5441] (4SWS VO, WS 2020/21)
Drton M