Robust estimation and outlier detection for varying-coefficient models via penalized regression

Varying-coefficient models (VCMs) are widely used in a variety of statistical applications. However, the classical VCMs based on least squares are prone to the presence of even a few severe outliers. In this article, a mean shift parameter is added for each observation to reflect outliers, and different penalties are then applied to the shift parameters to get sparse estimates. The jointly penalized optimization problem is solved through an efficient algorithm, and the tuning parameters are chosen by the Bayesian information criteria (BIC). The efficiency of the new approach is demonstrated via simulation studies as well as a real application on the Hong Kong environmental data.