Robust equivariant non parametric regression estimators for functional ergodic data

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

doi:10.1080/03610926.2019.1705980

Cited by 1 publication

(2 citation statements)

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“…We start by reminding the uniform asymptotic properties of µ(z, x, t(z)) defined in (2.6). The Theorem 4.1 defined bellow was proved by [2] in the special case when h L (z) = h L for all z ∈ T F , but their proof can be followed line by line under (4.2)). This general condition (4.2) will be a crucial preliminary tool for us.…”

Section: Resultsmentioning

confidence: 99%

“…In NFDA, kNN robustification equivariant nonparametric regression estimators for ergodic data is new. This researches's primary goal is to provide generalizations, to the kNN case, the results obtained by [2] in ergodic dependency case with the research of [38] and [1]. More precisely, we establish the almost complete convergence with rates of the constructed estimator by combining the ideas of robustness with those of smoothed regression.…”

Section: Introductionmentioning

confidence: 96%

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kNN robustification equivariant nonparametric regression estimators for functional ergodic data

SOMİA

WAHİBA

KADİ

et al. 2023

Hacettepe Journal of Mathematics and Statistics

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We discuss in this paper the robust equivariant nonparametric regression estimators for ergodic data with the k Nearst Neighbour (kNN) method. 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. Furthermore, a comparison study based on simulated data is also provided to illustrate the finite sample performances and the usefulness of the kNN approach and to prove the highly sensitive of the kNN approach to the presence of even a small proportion of outliers in the data.

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Section: Resultsmentioning

confidence: 99%