%0 Journal Article
%T Block thresholding in wavelet estimation of the regression function with errors in variables
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Shirazi, Esmaeil
%D 2023
%\ 09/01/2023
%V 14
%N 9
%P 367-377
%! Block thresholding in wavelet estimation of the regression function with errors in variables
%K Adaptive estimation
%K Block Theresholding Method
%K Errors-in-variables
%K Minimax estimation
%K Nonparametric regression
%K Wavelets
%R 10.22075/ijnaa.2023.28249.3821
%X Errors-in-variables regression is the study of the association between covariates and responses where covariates are observed with errors. In this paper, we consider the estimation of regression functions when the independent variable is measured with error. We investigate the performances of an adaptive wavelet block thresholding estimator via the minimax approach under the $L_p$ risk with $p \geq 1$ over Besov balls. We prove that it achieves the optimal rates of convergence.
%U https://ijnaa.semnan.ac.ir/article_7407_3c532e47b30f7d6c943e6bc265715080.pdf