Incomplete least squared regression function estimator based on wavelets

Ryma Douas, Ilhem Laroussi, Soumia Kharfouchi

Mentouri Brothers University Constantine, Algeria

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 $L_2$. 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.

Keywords: non-parametric regression, $L_2$ error, least squares estimators, orthogonal series estimates, convergence in the $L_2$-norm, twice censored data, regression estimation, hard thresholding.

UDC: 519.6

Received: 10.07.2022
Received in revised form: 15.09.2022
Accepted: 20.10.2022

Language: English