Elastic-Net Regression based on Empirical Mode Decomposition for Multivariate Predictors

Abstract

The empirical mode decomposition (EMD) method is used to decompose the non-stationary and nonlinear signal into a finite set of orthogonal non-overlapping time scale components that include several intrinsic mode function components and one residual component. Elastic net (ELN) regression is a statistical penalized method used to address multicollinearity among predictor variables and identify the necessary variables that have the most effect on the response variable. This study proposed the use of the ELN method based on the EMD algorithm to identify the decomposition components of multivariate predictor variables with the most effect on the response variable under multicollinearity problems. The results of the numerical experiments and real data confirmed that the EMD-ELN method is highly capable of identifying the decomposition components with the presence or absence of multicollinearity among the components. The proposed method also achieved the best estimation and reached the optimal balance between the variance and bias. The EMD-ELN method also improved the accuracy of regression modeling compared with the traditional regression models.