A Novel Robust M-Estimator for the Random-Coefficients Regression Model: Simulation and Its Application in Energy Management Systems | ||
| Computational Journal of Mathematical and Statistical Sciences | ||
| Articles in Press, Accepted Manuscript, Available Online from 12 October 2025 PDF (1.16 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/cjmss.2025.405428.1232 | ||
| Authors | ||
| Amr R Kamel* 1, 2; Mohamed R. Abonazel3; Ahmed H. Youssef1 | ||
| 1Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt | ||
| 2Department of Basic Sciences, El-Gazeera High Institute for Computers and Information Systems, Ministry of Higher Education, El-Mokattam 11571, Egypt | ||
| 3Department of applied statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo Uniersity, Giza 12613, Egypt | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Mean group estimator; Monte Carlo simulation; Non-robust estimators; Outliers; Panel data models; RCR model; Novel robust M-estimator; Swamy’s Estimator | ||
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