A Novel Robust M-Estimator for the Random-Coefficients Regression Model: Simulation and Its Application in Energy Management Systems

A random coefficient regression (RCR) model refers to a statistical model that incorporates random coefficients into degradation models, typically assumed to be normally distributed. An RCR model is a special type of panel data model. The RCR model provides a wide range of consequences for situations involving decision-making difficulties. The classical estimation methods for the RCR model perform well without outliers, but their performance degrades in the presence of outliers. To this end, this paper proposes a novel robust M-estimator with different objective functions and compares these with the non-robust (classical) estimators. The proposed robust M-estimators provide stable and reliable results even when outliers are present. A Monte Carlo simulation study and an empirical application to energy management systems were conducted to evaluate the performance of the non-robust RCR classical pooling (RCRCP) estimator, RCR mean group (RCRMG) estimator, and RCR Swamy’s (RCRSW) estimator, with the proposed robust M-estimators: RCR Huber (RCRHU), RCR Hampel (RCRHM), and RCR Bisquare (RCRBI). The findings from the simulation and application indicate that the proposed robust M-estimators outperform the non-robust estimators in the presence of outliers in the RCR model. Furthermore, the RCRBI estimator is more efficient than the other proposed robust M-estimators.