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 (WS 2022/23)
german english



Time and location
Exercises groups
Exercises sheets
Assessment
Lecture outline
References
Last edited on
2023/02/14 by jj
.
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:

DayTime 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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