kNN robustification equivariant nonparametric regression estimators for functional ergodic data

Authors : Guenani SOMİA, Bouabsa WAHİBA, Attouch MOHAMMED KADİ, Fetitah OMAR

Pages : 512-528

Doi:10.15672/hujms.1100871

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Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :We discuss in this paper the robust equivariant nonparametric regression estimators for ergodic data with the k Nearst Neighbour insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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.
Keywords : Functional data, ergodic data, kNN estimation, kernel estimate, uniform almost complete convergence rate, entropy