Exponential bounds for multivariate self-normalized sums
Patrice Bertail, Laboratory of Statistics, CREST and MODALX, University Paris X, France
Emmanuelle Gautherat, Laboratory of Statistics, CREST and Economic Faculty of Reims, France
Hugo Harari-Kermadec, Laboratory of Statistics, CREST and Université Paris-Dauphine, France
Abstract
In a non-parametric framework, we establish some non-asymptotic
bounds for self-normalized sums and quadratic forms in the
multivariate case for symmetric and general random variables. This
bounds are entirely explicit and essentially depends in the general
case on the kurtosis of the Euclidean norm of the standardized
random variables.
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