Abstract
AbstractWe derive non-asymptotic concentration inequalities for the uniform deviation between a multivariate density function and its non-parametric kernel density estimator in stationary and uniform mixing time series framework. We derive analogous inequalities for their (first) Wasserstein distance, as well as for the deviations between integrals of bounded functions w.r.t. them. They can be used for the construction of confidence regions, the estimation of the finite sample probabilities of decision errors, etc. We employ the concentration results to the derivation of statistical guarantees and oracle inequalities in regularized prediction problems with Lipschitz and strongly convex costs.
Funder
Athens University of Economics & Business
Publisher
Springer Science and Business Media LLC
Subject
Statistics and Probability
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