Abstract
We derive exponential inequalities for the oscillation of functions of random variables about their mean. This is illustrated on the Kolmogorov-Smirnov statistic, the total variation distance for empirical measures, the Vapnik-Chervonenkis distance, and various performance criteria in nonparametric density estimation. We also derive bounds for the variances of these quantities.
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Devroye, L. (1991). Exponential Inequalities in Nonparametric Estimation. In: Roussas, G. (eds) Nonparametric Functional Estimation and Related Topics. NATO ASI Series, vol 335. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3222-0_3
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DOI: https://doi.org/10.1007/978-94-011-3222-0_3
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