Optimizing bandwidth parameter estimation for non-parametric regression using fixed-form threshold with Dmey and Coiflet wavelets
Delshad Shaker Ismael Botani, Nazeera Sedeek Kareem, Taha Hussein Ali, Bekhal Samad Sedeeq · Hacettepe Journal of Mathematics and Statistics · 2025
The article aims to reduce the effect of data noise or outliers and estimate the optimal bandwidth parameter used in nonparametric regression models using a proposed method based on wavelet analysis, specifically Dmey and Coiflet wavelets with fixed-form threshold and apply the soft threshold, particularly when the data have long-tailed and multimodal distributions (abnormal distribution). The fixed-form threshold level value estimates the bandwidth instead of the classical method (geometric, arithmetic mean, range, and median). A simulation study was used to examine the suggested method, comparing it with four other Nadaraya-Watson kernel estimators (classical techniques), using a MATLAB language created especially for this purpose with actual data. The findings show that the suggested method outperforms classical methods for all cases of simulations and real data in accurately estimating the bandwidth parameter of the non-parametric regression kernel function based on the mean square error criterion.