On Selection of Semiparametric Spatial Regression Models

TL;DR

This paper introduces a novel variable selection method for semiparametric spatial regression models that effectively handles irregular spatial domains and identifies significant covariates with oracle properties.

Contribution

The paper develops a unified double penalization framework for variable selection in semiparametric spatial models using bivariate splines over triangulation, ensuring accurate covariate identification.

Findings

Method accurately identifies significant spatial covariates.

Simulation studies demonstrate the effectiveness of the approach.

Real data application confirms practical utility.

Abstract

In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial smoothing problem in the nonparametric part is tackled by means of bivariate splines over triangulation, which is able to deal efficiently with data distributed over irregularly shaped regions. In addition, we develop a unified procedure for variable selection to identify significant covariates under a double penalization framework, and we show that the penalized estimators enjoy the "oracle" property. The proposed method can simultaneously identify non-zero spatially distributed covariates and solve the problem of "leakage" across complex domains of the functional spatial component. To estimate the standard deviations of the proposed estimators for the coefficients, a sandwich formula is developed as well. In the end, Monte Carlo simulation examples and a real data example are provided to illustrate the proposed methodology. All technical proofs are given in the supplementary materials.