Univ. Heidelberg
Statistics Group   Institute of Applied Mathematics   Faculty of Mathematics and Computer Science   University Heidelberg
Ruprecht-Karls-Universität Heidelberg Statistics of inverse problems Research Group Lecture course Statistics 2 (SS 2020)
german english

Time and location
Exercises groups
Exercises sheets
Lecture outline
Last edited on
2020/07/23 by jj
Time and location of the lecture course:
Wednesday 11:15-12:45 and Friday; 09:15-10:45
The lecture will take place online using heiCONF.
Please register by using MÜSLI to obtain further details by email.


day time location
Wednesday, 07/29/2020 10:30-13:15 MΛTHEMΛTIKON, INF 205, Hörsaal
Please hand over the signed formular on your arrival. Please read the informations on data protection and be aware of the access and attendance prohibition.

Lecturer: Prof. Dr. Jan JOHANNES <johannes[at]math.uni-heidelberg.de>
Assistent: Sergio Brenner Miguel <brennermiguel[at]math.uni-heidelberg.de>
Questions, please directly by email or by using the contact form.

The lecture will be given in English if there is at least one non-German speaking participant.

Exercise group:
Please register for the exercise group of Statistics 2 by using MÜSLI
to obtain further details by eMail.
We propose the following exercise group:

Thursday 09:00-11:00online Ricardo Blum
Questions, please directly to Ricardo by using MÜSLI.

Exercise sheets:
The exercise sheets will be published every Monday morning at 09:00 a.m. starting with April 27th, 2020.
Please upload your solution proposals 7 days later monday before 09:00 a.m. on Moodle.
Please register by using MÜSLI to obtain further details by eMail.
The exercise should be handed over in fixed groups of two.

Exercise sheet: UE01 UE02 UE03 UE04 UE05 UE06
Handing in: 05/04/2020 05/11/2020 05/18/2020 05/25/2020 06/02/2020 06/15/2020
Exercise sheet: UE07 UE08 UE09 UE10 UE11
Handing in: 06/22/2020 06/29/2020 07/06/2020 07/13/2020 07/20/2020

Admission requirements and final grade:
The written examinartion will solely determine the final grade. You have to pass the written examination, in order to successfully attend the modul.

day time location
First examination Wednesday 07/29/2020 11:00-13:00 MΛTHEMΛTIKON, INF 205, Hörsaal
Admission requirements:
  • Accepted for the written examination is someone who either
    • has achieved at least 50% of the points of the exercises and
  • or
    • was accepted for a written examination of a previous lecture named Statistics 2 and
    • has not lost the examination claim.
Grading rules:
  • The first and the second exam together are counted as one examination attempt. The modul Statistics 2 is considered as failed if one fails in both of the exams. The final mark of the modul is the mark of the first passed exam.
  • Students who attempt the first exam and pass with a mark better then 4.0, cannot attempt the second exam.
  • Only those students are allowed to attempt the second exam who failed the first exam (either with the mark 5.0 or by not attempting). It is not possible to participate in the second exam to improve the mark.

Lecture outline:
The outline of the lecture (sections §01-§17, 07/21/2020) is published before the lecture takes place. All lecture notes can be found as soon as possible after the lecture separately on Moodle as well as combined Part A and Part B. A recording of the lecture for each section separately can be found on Moodle. In the following table the individual documents are ordered by subjects.

outline note screencast
Chap 1 Preliminaries
§01 Fundamentals le01-§01
§02 Convergence of random variables le01 le01-§02
§03 Conditional expectation le02-§03
Chap 2 M- and Z-estimator
§04 Introduction / motivation / illustration le02 le03 le02-§04.1 le03-§04.2 le03-§04.3
§05 Consistency le04 le04-§05.1 le04-§05.2 le05-§05.3
§06 Asymptotic normality le05 le05-§06.1 le06-§06.2
Chap 3 Asymptotic properties of tests
§07 Contiguity le06 le07 le08 le09 le06-§07.1 le07-§07.2 le07-§07.3 le08-§07.4 le08-§07.5 le09-§07.6 le09-§07.7 le10-§07.8
§08 Local asymptotic normality (LAN) le10 le11 le12 le010-§08.1 le011-§08.2 le011-§08.3 le012-§08.4 le012-§08.5
§09 Asymptotic relative efficiency (ARE) le13 le013-§09
§10 Rank tests le14 le013-§10.1 le014-§10.2 le014-§10.3
§11 Asymptotic power of rank tests le15 le015-§11.1 le015-§11.2
Chap 4 Nonparametric estimation Sec. §01-§17 (07/21/2020)
§12 Introduction le016-§12
§13 Kernel density estimation le16 le17 le18 le016-§13.1 le017-§13.2 le017-§13.3 le018-§13.4 le018-§13.5
§14 Nonparametric regression by local smoothing le19 le019-§14.1 le019-§14.2 le020-§14.3
§15 Sequence space model le20 le21 le22 le020-§15.1 le021-§15.2 le021-§15.3 le022-§15.4 le022-§15.5
§16 Orthogonal series estimation le23 le24/25 le023-§16.1 le023-§16.2 le024-§16.3 le024-§16.4
§17 Supplementary materials

Bickel and Doksum: Mathematical Statistics: Basic Ideas and Selected Topics. (Volume 1. Prentice Hall, London, 2001)
Comte: Estimation non-paramétrique. (Spartacus-idh, Paris, 2015)
Giné and Nickl: Mathematical foundations of infinite-dimensional statistical models. (Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, 2016)
Klenke: Wahrscheinlichkeitstheorie. (Springer Spektrum, 3., überarbeitete und ergänzte Auflage, 2012.)
Lehmann and Casella: Theory of Point Estimation. (Springer, New York, 1998)
Lehmann and Romano: Testing Statistical Hypotheses. (Springer, New York, 2005)
Tsybakov: Introduction to nonparametric estimation. (Springer Series in Statistics. Springer, New York, 2009)
van der Vaart: Asymptotic statistics. (Cambridge University Press, 1998)
Witting: Mathematische Statistik I. Parametrische Verfahren bei festem Stichprobenumfang. (Stuttgart: B. G. Teubner, 1985)
Witting and Müller-Funk: Mathematische Statistik II. Asymptotische Statistik: Parametrische Modelle und nichtparametrische Funktionale. (Stuttgart: B. G. Teubner, 1995)

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