University Heidelberg | SIP RG | Lecture course Statistics 2 (WS 2022/23)

Time and location of the lecture course:

Wednesday 09:15-10:45 and Friday 09:15-10:45, MΛTHEMΛTIKON, INF 205, SR B
Timely announcement about the lecture you receive on Moodle.
Please register by using Müsli to obtain further details by email.

Contact:

Lecturer: Prof. Dr. Jan JOHANNES <johannes[at]math.uni-heidelberg.de>

Assistent: Bianca Neubert <neubert[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	MΛTHEMΛTIKON (INF 205)	Instructor
Thursday	09 - 11 am	Seminarraum 3	Maximilian Siebel

Questions, please directly to Maximilian by using Müsli.

Exercise sheets:

Please upload your solution proposals every tuesday before 09:00 a.m. online on Moodle.
The exercise should be handed over in fixed groups of three.
The name of the uploaded file should have the form Name1_Name2_Name3_Sheet3.pdf.
Please register by using Müsli to obtain further details by eMail.


Exercise sheet:	UE01	UE02	UE03	UE04	UE05	UE06
Handing in:	11/01/2022	11/08/2022	11/15/2022	11/22/2022	11/29/2022	12/06/2022
Solutions outline:	L01.pdf	L02.pdf	L03.pdf	L04.pdf	L05.pdf	L06.pdf

Exercise sheet:	UE07	UE08	UE09	UE10	UE11	UE12
Handing in:	12/13/2022	12/20/2022	01/17/2023	01/24/2023	01/31/2023	02/07/2023
Solutions outline:	L07.pdf	L08.pdf	L09.pdf	L10.pdf	L11.pdf	L12.pdf

Admission requirements and final grade:

The written examination will solely determine the final grade. You have to pass the written examination, in order to successfully attend the modul. If you have any doubts, please contact us as soon as possible.

Admission requirements:

Accepted for the written examination is someone who either
- has achieved at least 50% of the points of the exercises and
- has actively participated during the exercises
or
- was accepted for a written examination of a previous lecture named Statistics 2 and has not lost the examination claim.

Grading rules:

There will be two written examination (probably in the beginning and end of the lecture free time). The first and the second exam is counted each as one examination attempt. 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 attending). It is not possible to participate in the second exam to improve the mark.

Lecture outline:

The outline of the lecture (sections §01-§22, 02/01/2023) is published before the lecture takes place. All lecture notes can be found as soon as possible after the lecture separately on here as well as combined Part A (Le01-Le09a), Part B (Le09b-Le17a) and Part C (Le17b-Le25). In the following table the individual documents are ordered by subjects.

		outline	note
Chap 1	M- and Z-estimator
§01	Introduction
§02	Consistency		le01
§03	Asymptotic normality		le02
Chap 2	Asymptotic properties of tests
§04	Contiguity		le03 le04
§05	Local asymptotic normality (LAN)		le05 le06
§06	Asymptotic relative efficiency (ARE)		le07
§07	Rank tests
§08	Asymptotic power of rank tests		le08 le09a
Chap 3	Nonparametric estimation by projection
§09	Review
§10	Noisy version of the parameter		le09b
§11	Orthogonal projection		le10
§12	Orthogonal projection estimator		le11 le12
§13	Minimax optimal estimation		le13 le14
§14	Data-driven estimation		le15 le16 le17a

Chap 4	Nonparametric density estimation
§15	Noisy density coefficients		le17b
§16	Projection density estimator		le18
§17	Minimax optimal density estimation		le19
§18	Data-driven density estimation		le20 le21

Chap 5	Nonparametric regression	§01-§22	(02/01/2023)
§19	Noisy regression coefficients		le22
§20	Projection regression estimator		le23
§21	Minimax optimal regression/td>		le24
§18	Data-driven regression		le25

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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