Structure identification and model selection in geographically weighted quantile regression models

Geographical weighted quantile regression (GWQR) is an important tool for exploring the spatial non-stationarity of the regression relationship and providing the entire description of the response distribution, which is useful in practice because of its robustness against outliers and flexibility in dealing with non-normal distributions. This paper proposes the GWQlasso method for structure identification and variable selection in GWQR models. The proposed method combines the local-linear estimation of the GWQR model and the adaptive group lasso, which can simultaneously identify spatially varying coefficients, non-zero constant coefficients and zero coefficients. The selection consistency and the oracle property of the proposal are studied. Moreover, the derived algorithm for the GWQlasso method and the selection of the tuning parameter by the BIC criterion are established. Simulations and real examples are used to illustrate the method.