Robust equivariant non parametric regression estimators for functional ergodic data

Ibrahim M. Almanjahie, Mohammed Kadi Attouch, Zoulikha Kaid and Hayat Louhab

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 15, 3505-3521

Abstract: This article deals with the equivariant non parametric robust regression estimation for stationary ergodic processes valued in F×R, where F is a semi-metric space. We consider a new robust regression estimator when the scale parameter is unknown. The principal aim is to prove the almost complete convergence (with rate) for the proposed estimator. Unlike in standard multivariate cases, the gap between pointwise and uniform results is not immediate. So, suitable topological considerations are needed, implying changes in the rates of convergence which are quantified by entropy considerations.

Date: 2021
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DOI: 10.1080/03610926.2019.1705980

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