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2008 Exponential bounds for multivariate self-normalized sums
Patrice Bertail, Emmanuelle Gautherat, Hugo Harari-Kermadec
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Electron. Commun. Probab. 13: 628-640 (2008). DOI: 10.1214/ECP.v13-1430


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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Patrice Bertail. Emmanuelle Gautherat. Hugo Harari-Kermadec. "Exponential bounds for multivariate self-normalized sums." Electron. Commun. Probab. 13 628 - 640, 2008.


Accepted: 14 December 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1186.62068
MathSciNet: MR2466190
Digital Object Identifier: 10.1214/ECP.v13-1430

Primary: 62G15
Secondary: 62E17 , 62H15

Keywords: Exponential inequalities , Hoeffding inequality , multivariate , self-normalization

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