Robust Model Averaging Method Based on LOF Algorithm (Communications in Mathematical Research, 2023)
Model averaging is a good alternative to model selection, which candeal with the uncertainty from model selection process and make full use ofthe information from various candidate models. However, most of the existing model averaging criteria do not consider the influence of outliers on theestimation procedures. The purpose of this paper is to develop a robust modelaveraging approach based on the local outlier factor (LOF) algorithm whichcan downweight the outliers in the covariates. Asymptotic optimality of theproposed robust model averaging estimator is derived under some regularityconditions. Further, we prove the consistency of the LOF-based weight estimator tending to the theoretically optimal weight vector. Numerical studiesincluding Monte Carlo simulations and a real data example are provided toillustrate our proposed methodology.