Variable selection for spatial nonparametric regression

Abstract

Spatial varying coefficient regression model is an important generalization of spatial linear regression model. It is useful in real application. However, how to make variable selection for it has not been well studied. In this paper, a general M-type loss function is used to treat mean, median, quantile and robust mean regressions in one setting. Then by B-spline approximation, we propose an adaptive group L r ( r ≥1) penalized M-type estimator, which can select relevant variables and estimate functional coefficients simultaneously. Moreover, it has several distinctive features: (1) It achieves robustness against outliers and heavy-tail distributions; (2) it is more flexible to accommodate heterogeneity and allows the set of relevant variables to vary across quantiles; (3) it can keep balance between efficiency and robustness. Under mild conditions, the oracle property is established. Simulation studies and real data analysis are conducted to assess the finite sample property of the proposed method.