Mathematical Colloquium
Upcoming talks:
| Tue 16 Jun 2026, 16:30: Shahar Mendelson (Texas A&M University) Mean estimation and beyond |
| Consider an unknown random vector X, taking values in R^d. Is it possible to "guess" its mean accurately if the only information one is given consists of N independent copies of X? More accurately, given an arbitrary norm on R^d, the goal is to find a mean estimation procedure: upon receiving a wanted confidence parameter \delta and N independent copies X_1,...,X_N of an unknown random vector X - that has a finite mean and covariance -, the procedure returns \hat{\mu} for which the error \| \hat{\mu} - E X\| is as small as possible with probability at least 1-\delta (with respect to the product measure). The mean estimation problem has been studied extensively over the years and I will present some of the ideas that have led to its solution (and to the solution of other questions of a similar flavour that I will outline). Two surprising facts are that in all these problems the obvious choices fail miserably (for mean estimation, that choice is N^{-1}\sum_{i=1}^N X_i); and, that the solution behaves as if the (arbitrary) random vector X were gaussian. ________________________________________ Invited by Prof. Holger Rauhut |
| Theresienstr. 39, München. Room A 027 |
| Tue 21 Jul 2026, 16:30: Kotaru Komatsu (University of Tsukuba) TBA |
| TBA |
| Theresienstr. 39, München. Room A 027 |
All lectures are on Tuesdays at 4:30 pm in lecture hall A027 unless otherwise noticed.
Looking for past events? You may find them in the Munich Mathematical Calendar.