New Robust M-Estimator for Random-Coefficients Panel Data Model: Algorithms, Simulation, and Application to Insurance Data

This paper proposes a new class of M-estimators based on an innovative objective function that provides highly robust and efficient estimates. The resulting estimator, referred to as the robust AKY estimator, is introduced as an alternative to the random coefficient regression (RCR) estimator in the presence of outliers. The results show that, for normal and clean data, the proposed robust AKY estimator performs almost as well as the RCR estimator. However, it demonstrates significantly greater resistance to outliers when applied to contaminated datasets within the random coefficients panel data (RCPD) model. To evaluate its performance, a Monte Carlo simulation study was conducted under various data-generation scenarios with different levels of outlier contamination. The results were compared with those of the non-robust RCR estimator and several existing robust M-estimators, including Huber, Hampel, Andrew, and Bisquare. In addition, the proposed robust AKY estimator was evaluated using a real insurance dataset. The findings from both the simulation study and the empirical application indicate that the robust estimators (Huber, Hampel, Andrew, Bisquare, and AKY) outperform the RCR estimator in the presence of outliers in the RCPD model. Moreover, the proposed robust AKY estimator is more efficient than the other robust M-estimators.