A robust regression methodology is proposed via M-estimation. The approach adapts to the tail behavior and skewness of the distribution of the random error terms, providing for a reliable analysis under a broad class of distributions. This is accomplished by allowing the objective function, used to determine the regression parameter estimates, to be selected in a data driven manner. The asymptotic properties of the proposed estimator are established and a numerical algorithm is provided to implement the methodology. The finite sample performance of the proposed approach is exhibited through simulation and the approach was used to analyze two motivating datasets.
Keywords: Asymmetric exponential power distribution; Linear regression; M-estimation; Quantile regression; Robust regression.