Journal of Siberian Federal University. Mathematics & Physics / Incomplete Least Squared Regression Function Estimator Based on Wavelets

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2023 16 (2)
Authors
Ryma Douas; Ilhem Laroussi; Soumia Kharfouchi
Contact information
Ryma Douas: Sciences Laboratory Department of Mathematics Mentouri Brothers University Constantine, Algeria; ; Ilhem Laroussi: Sciences Laboratory Department of Mathematics Mentouri Brothers University Constantine, Algeria; ; Soumia Kharfouchi: Department of Mathematics Laboratory of Mathematical Biostatistics Bioinformatics and Methodology Applied to Health Sciences Mentouri Brothers University Constantine, Algeria;
Keywords
non-parametric regression; L2 error; least squares estimators; orthogonal series estimates; convergence in the L2-norm; twice censored data; regression estimation; hard thresholding
Abstract

In this paper, we introduce an estimator of the least squares regression function, for Y right censored by R and min(Y;R) left censored by L. It is based on ideas derived from the context of wavelet estimates and is constructed by rigid thresholding of the coefficient estimates of a series development of the regression function. We establish convergence in norm L2. We give enough criteria for the consistency of this estimator. The result shows that our estimator is able to adapt to the local regularity of the related regression function and distribution

Pages
204–215
EDN
GVQDEI
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/149916