University Heidelberg | SIP RG | Lecture course Statistics 2 (SS 2020)

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.

Examination:

	day	time	location
Second examination	Friday, 10/23/2020	08:??-11:00	MΛTHEMΛTIKON, INF 205, Hörsaal
First examination	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.

Contact:

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.

Language:

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:

Day	Time	Location	Instructor
Thursday	09:00-11:00	online	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
Second examination	Friday	10/23/2020	08:??-11:00	MΛTHEMΛTIKON, INF 205, Hörsaal
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

References:

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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