Wavelet Analysis for Outlier Estimation in Multivariate Linear Regression Models

Abstract
Outliers significantly impact parameter estimation accuracy in multivariate linear regression models, so traditional methods, such as the Hampel filter, are used to address this problem. This study proposes a wavelet-based approach to address outliers by estimating these values based on the discrete wavelet transform (DWT) of the wavelets (Daubechies, Coiflets, and Dmey) and calculating the approximation and detail coefficients (Low and High pass filter, respectively) which used in estimating the parameters of the multivariate regression model for the approximation and detail coefficients and through these models the predictive values of these coefficients calculated the inverse of the discrete wavelet transform of the predictive values taken to obtain the filtered observations. Then, the filtered predictive values corresponding to the outliers are the estimated observations that address the outlier problem. The accuracy of the estimated parameters of the multivariate linear regression model using the proposed methods and the Hampel filter was compared through some accuracy criteria of the estimated models, including the mean absolute error (MAE) of the estimated parameters, mean squared error (MSE), and coefficient of determination (R²)). Simulation experiments and real-world blood test data confirm the superiority of the wavelet-based approach, decreasing MSE by 0.7728 and improving R2 by 83.19% for Y1, (74.33%) for Y2, and (87.50%) for Y3, compared to the Hampel filter. These results demonstrate that wavelet-based filtering provides a more robust and accurate alternative for handling outliers in multivariate regression models.