401-4627-00L  Empirical Process Theory and Applications

SemesterSpring Semester 2022
LecturersS. van de Geer
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-4627-00 VEmpirical Process Theory and Applications2 hrs
Wed08:15-10:00HG D 5.2 »
S. van de Geer

Catalogue data

AbstractEmpirical process theory provides a rich toolbox for studying the properties of empirical risk minimizers, such as least squares and maximum likelihood estimators, support vector machines, etc.
Objective
ContentIn this series of lectures, we will start with considering exponential inequalities, including concentration inequalities, for the deviation of averages from their mean. We furthermore present some notions from approximation theory, because this enables us to assess the modulus of continuity of empirical processes. We introduce e.g., Vapnik Chervonenkis dimension: a combinatorial concept (from learning theory) of the "size" of a collection of sets or functions. As statistical applications, we study consistency and exponential inequalities for empirical risk minimizers, and asymptotic normality in semi-parametric models. We moreover examine regularization and model selection.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits4 credits
ExaminersS. van de Geer
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
Additional information on mode of examinationBitte beachten Sie, dass diese Prüfung letztmalig in der Sommersession 2023 angeboten wird.

Please note that this exam will be offered for the last time in the summer examination session 2023
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

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Only public learning materials are listed.

Groups

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Restrictions

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Offered in

ProgrammeSectionType
Data Science MasterCore ElectivesWInformation
Mathematics BachelorSelection: Probability Theory, StatisticsWInformation
Mathematics MasterSelection: Probability Theory, StatisticsWInformation
Statistics MasterStatistical and Mathematical CoursesWInformation
Statistics MasterSubject Specific ElectivesWInformation