B1803
Title: New bounds for self-normalized sums in high dimensional settings
Authors: Emmanuelle Gautherat - University of Reims (France) [presenting]
Patrice Bertail - University of Paris-Ouest-Nanterre-La Defense (France)
El Mehdi Issouani - University Paris Nanterre (France)
Abstract: The aim is to present some bounds for self-normalized sums in a multidimensional setting. In many applications, dimension q of the observed random vector is large in comparison to sample size n and sometimes increases with n. In that case, the main problem lies in the fact that the empirical covariance matrix is not full rank. Many authors have discussed this problem and have proposed some bounds - or limits - in that case under some strong assumptions (normality, symmetry of the distribution etc.). However, there is no guarantee that such a structure holds in practice. It is proposed to recall some existing results and to present new exact bounds for self-normalized sums in high-dimensional settings with general distribution.
