Effect of Denoising Dependent and Independent Variables On the Performances of NonLinear Regression Parameters of the Estimators

Denosing is any signal processing method which reconstructs a signal from a noisy one. Its goal is to remove noise and preserve useful information. In the study simulated data under three (3) sample sizes (i.e 32,256 and 1024) were used, applying Epanechnikov kernel Gaussian kernel, Wavelet and Polynomial Spline to denoise the variables in two approaches. The study revealed the performances of denoised nonlinear estimators under different sample sizes and comparison was made using the mean squared error criterion. The result of the studies showed that the approach of denoising both the dependent and independent variables enhance the performances of non-linear least squares estimator (DNLS) under each sample size for the different four smoothers considered.