Block thresholding in wavelet estimation of the regression function with errors in variables

Document Type : Research Paper


1 Department of Statistics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous 4971799151, Iran

2 Department of Statistics, Payame Noor University, P. O. Box 19395-4697, Tehran, Iran


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.


Articles in Press, Corrected Proof
Available Online from 05 February 2023
  • Receive Date: 16 March 2022
  • Revise Date: 05 July 2022
  • Accept Date: 10 September 2022
  • First Publish Date: 05 February 2023