Abstract:
In statistics and econometrics, it has been a challenging problem to construct consistent
estimators of the parameters in a nonlinear regression model due to the presence of
measurement error in the data.
This study shows, using simulated data, that applying kernel, wavelet and the proposed
polynomial spline denoising on noisy data in the context of a nonlinear regression model can overcome this limitation. It shows the linearization of a nonlinear model solved by a successive linear approximation based on linear Taylor series.
A class of denoised nonlinear regression is suggested for a nonlinear measurement error model.
This study also presents a comparative study of the performance of denoised nonlinear
estimators under different smoothing techniques. Simulation studies are carried out to illustrate the performance of these estimators which are compared based on the mean squared error criterion. The result of the studies shows that the denoised nonlinear least squares estimator outperforms both denoised nonlinear least absolute deviation estimator and denoised nonlinear M-estimator under each of the smoothers considered.
