Document Type : Research Paper

Authors

• Esmaeil Shirazi ¹
• Bahareh Ghanbari ²

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

Abstract

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.

Keywords

• Adaptive estimation
• Block Theresholding Method
• Errors-in-variables
• Minimax estimation
• Nonparametric regression
• Wavelets