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2014 Adaptive and minimax estimation of the cumulative distribution function given a functional covariate
Gaëlle Chagny, Angelina Roche
Electron. J. Statist. 8(2): 2352-2404 (2014). DOI: 10.1214/14-EJS956

Abstract

We consider the nonparametric kernel estimation of the conditional cumulative distribution function given a functional covariate. Given the bias-variance trade-off of the risk, we first propose a totally data-driven bandwidth selection mechanism in the spirit of the recent Goldenshluger-Lepski method and of model selection tools. The resulting estimator is shown to be adaptive and minimax optimal: we establish nonasymptotic risk bounds and compute rates of convergence under various assumptions on the decay of the small ball probability of the functional variable. We also prove lower bounds. Both pointwise and integrated criteria are considered. Finally, the choice of the norm or semi-norm involved in the definition of the estimator is also discussed, as well as the projection of the data on finite dimensional subspaces. Numerical results illustrate the method.

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Gaëlle Chagny. Angelina Roche. "Adaptive and minimax estimation of the cumulative distribution function given a functional covariate." Electron. J. Statist. 8 (2) 2352 - 2404, 2014. https://doi.org/10.1214/14-EJS956

Information

Published: 2014
First available in Project Euclid: 6 November 2014

zbMATH: 1302.62082
MathSciNet: MR3275747
Digital Object Identifier: 10.1214/14-EJS956

Subjects:
Primary: 62G05
Secondary: 62H12

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

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