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Exponential bounds for multivariate self-normalized sums
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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
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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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Full text: PDF
Pages: 628-640
Published on: December 14, 2008
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Electronic Communications in Probability. ISSN: 1083-589X |
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