Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 10th of May 2021
Place: Visio
Gabor LUGOSI (Pompeu Fabra University) – “Mean estimation in high dimensions ”

Abstract: We consider the problem of estimating the mean of a random vector based on independent, identically distributed observations. In particular, we are interested in estimators that are close to the true mean vector in all directions. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance of the one dimensional marginal of the random vector is not too small. The random vector may have a heavy-tailed distribution.

The proof relies on novel uniform bounds for the ratio of empirical and true probabilities.

The talk is based on joint work with Shahar Mendelson.

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Zoltan SZABO (CMAP)
Sponsors:
CREST-CMAP