The mixed ridge is evaluated using wavelet analysis as an alternative to conventional penalized approaches (simulation study)

Abstract—In this research, we use threshold wavelet approaches to estimate tuning parameters in the presence of the contamination problem (noise) for calculated parameters in multiple linear regression. To estimate tuning parameters, the suggested technique uses wavelet shrinkage (for wavelets family, Symlets and Fejer-Korovkin and threshold, Universal, SURE, and Minimax). It is also utilized in penalized methods for variable selection and linear model coefficient estimation. Using simulation experiments for contamination levels of 10% and 25% as well as actual data, in contrast to the conventional penalized method, this study presents a straightforward estimate for parameter adjustment based on the penalized method's wavelet shrinkage (Ridge). The results of using the statistical criteria (MAE and MSE) to compare the suggested technique to a traditional penalized method. The penalized technique's wavelet shrinkage produces the best results and is more precise than the conventional approach in all simulations, according to the MAE and MSE criteria. Keywords—Ridge regression, Wavelet Shrinkage, Threshold, Wavelet Ridge, and the penalized technique.