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Varying coefficient regression is a flexible technique for modeling datawhere the coefficients are functions of some effect-modifying parameter, oftentime or location in a certain domain. While there are a number of methods forvariable selection in a varying coefficient regression model, the existingmethods are mostly for global selection, which includes or excludes eachcovariate over the entire domain. Presented here is a new local adaptivegrouped regularization (LAGR) method for local variable selection in spatiallyvarying coefficient linear and generalized linear regression. LAGR selects thecovariates that are associated with the response at any point in space, andsimultaneously estimates the coefficients of those covariates by tailoring theadaptive group Lasso toward a local regression model with locally linearcoefficient estimates. Oracle properties of the proposed method are establishedunder local linear regression and local generalized linear regression. Thefinite sample properties of LAGR are assessed in a simulation study and forillustration, the Boston housing price data set is analyzed.

Local Adaptive Grouped Regularization and its Oracle Properties for Varying Coefficient Regression