Wavelet shrinkage in estimation of regression function with error in variables

The purpose of this study was to estimate the unknown regression function h in a regression model having errors-in-variables: (Y,X), where Y=h(U)+E and X=U+T. We propose a new adaptive estimator through the wavelet shrinkage method to estimate h. In particular, the block thresholding method has been investigated by considering some simple assumptions on E. Finally, using a simulation study, we have compared the proposed estimator with other threshold estimators.

Keywords:

Block Thresholding Method , Error in Variable , Nonparametric regression , Shrinkage Method , Wavelets