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Exponential bounds for multivariate self-normalized sums. (English) Zbl 1186.62068
Summary: In a nonparametric framework, we establish some non-asymptotic bounds for self-normalized sums and quadratic forms in the multivariate case for symmetric and general random variables. These bounds are entirely explicit and essentially depend in the general case on the kurtosis of the Euclidean norm of the standardized random variables.

MSC:
62H10 Multivariate distribution of statistics
62G99 Nonparametric inference
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