Development of a Robust Partial Least Squares Regression Approach Incorporating Wavelet Transformation

This paper develops a hybrid statistical framework using Robust Partial Least Squares Regression (RPLSR) with wavelet analysis to increase model accuracy and stability under noisy and high-dimensional conditions. Classical Partial Least Squares Regression (PLSR) is famous for being sensitive to multicollinearity but also sensitive to outliers and data irregularities. The proposed solution addresses these limitations, with robust estimation procedures and wavelet-based denoising from Daubechies, Coiflets, and Discrete Meyer wavelets. Several sample sizes and predictors were used in the simulation to determine performance by MSE and R2 through the means of varying sampling size and predictor size of predictors. The results showed that all wavelet-enhanced RPLSR variants significantly improve estimation accuracy and increase predictive power, with an R2 of over 97% in some cases. The model is further validated by real data from Al-Zahraa Hospital in Iraq, as well as full blood count observations in complete blood samples at the Al-Zahraa Hospital, where the methodology was tested for robustness and interpretability. In general, robust regression with wavelet preprocessing provides a powerful, flexible, and noise-resilient framework for analyzing complex biomedical, environmental, and financial datasets.