Robust variable selection with exponential squared loss for the partially linear varying coefficient spatial autoregressive model

The partially linear varying coefficient spatial autoregressive model is a semi-parametric spatial autoregressive model in which the coefficients of some explanatory variables are variable, while the coefficients of the remaining explanatory variables are constant. For the nonparametric part, a local linear smoothing method is used to estimate the vector of coefficient functions in the model, and, to investigate its variable selection problem, this paper proposes a penalized robust regression estimation based on exponential squared loss, which can estimate the parameters while selecting important explanatory variables. A unique solution algorithm is composed using the block coordinate descent (BCD) algorithm and the concave-convex process (CCCP). Robustness of the proposed variable selection method is demonstrated by numerical simulations and illustrated by some housing data from Airbnb.