Course ObjectiveTo study the statistical properties of estimators in the context of
models with an unknown parameter vector that is very high-dimensional
compared to sample size. The assessment of the theory and the ability to
apply the theory in practical illustrations.
Course ContentIn statistics courses, the focus is on statistical models in which the
number of unknown parameters is small relative to the sample size.
Typical estimation results imply that, as the sample size n increases to
infinity, maximum likelihood estimators converge at the rate n^(1/2) to
the parameter corresponding to the true distribution that generated the
data (under certain regularity conditions). Furthermore, asymptotically
such estimators are normally distributed and efficient, in the sense
that they have minimal asymptotic variance. In this course we consider
models with an unknown parameter that is very high-dimensional compared
to sample size, or even infinite-dimensional. Here estimators have
completely different behavior: convergence rates are typically slower
than n^(1/2), asymptotic normality is not guaranteed, and optimality of
procedures cannot be assessed in terms of minimal asymptotic variance.
This course provides an introduction to the mathematics of
high-dimensional statistical models with applications.
Teaching MethodsWe have 4 hours of lectures and 2 hours of tutorial lectures.
Method of AssessmentWritten exam
Recommended background knowledgeStatistics, Multivariate Statistics, Machine Learning, Data Science
|Language of Tuition||English|
|Faculty||School of Business and Economics|
|Course Coordinator||E.A. Beutner|
You need to register for this course yourself
Last-minute registration is available for this course.
|Teaching Methods||Lecture, Study Group|
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