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November 2018 Robust dimension-free Gram operator estimates
Ilaria Giulini
Bernoulli 24(4B): 3864-3923 (November 2018). DOI: 10.3150/17-BEJ981


In this paper, we investigate the question of estimating the Gram operator by a robust estimator from an i.i.d. sample in a separable Hilbert space and we present uniform bounds that hold under weak moment assumptions. The approach consists in first obtaining non-asymptotic dimension-free bounds in finite-dimensional spaces using some PAC-Bayesian inequalities related to Gaussian perturbations of the parameter and then in generalizing the results in a separable Hilbert space. We show both from a theoretical point of view and with the help of some simulations that such a robust estimator improves the behavior of the classical empirical one in the case of heavy tail data distributions.


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Ilaria Giulini. "Robust dimension-free Gram operator estimates." Bernoulli 24 (4B) 3864 - 3923, November 2018.


Received: 1 November 2015; Revised: 1 December 2016; Published: November 2018
First available in Project Euclid: 18 April 2018

zbMATH: 06869894
MathSciNet: MR3788191
Digital Object Identifier: 10.3150/17-BEJ981

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability


Vol.24 • No. 4B • November 2018
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