  Varying coefficient regression is a flexible technique for modeling data
where the coefficients are functions of some effect-modifying parameter, often
time or location in a certain domain. While there are a number of methods for
variable selection in a varying coefficient regression model, the existing
methods are mostly for global selection, which includes or excludes each
covariate over the entire domain. Presented here is a new local adaptive
grouped regularization (LAGR) method for local variable selection in spatially
varying coefficient linear and generalized linear regression. LAGR selects the
covariates that are associated with the response at any point in space, and
simultaneously estimates the coefficients of those covariates by tailoring the
adaptive group Lasso toward a local regression model with locally linear
coefficient estimates. Oracle properties of the proposed method are established
under local linear regression and local generalized linear regression. The
finite sample properties of LAGR are assessed in a simulation study and for
illustration, the Boston housing price data set is analyzed.
