|
Abstract:
|
In this paper, we introduce a new class of generalized additive partially linear spatial models (GAPLSMs) for spatial data distributed over complex domains. By extending the classical generalized additive models, we incorporate linear terms, univariate spline components, and the spatial component into one unified model. We employ the regularization technique with the SCAD penalty to identify the linear and nonlinear components, use univariate polynomial splines to approximate the univariate functions, and apply bivariate penalized splines over triangulation to adjust the spatial effects. Based on the model identification and estimation results, we make the inference of univariate nonlinearities by applying the back-fitting idea into a penalized quasi-likelihood framework. We investigate the consistency of the proposed estimators and the asymptotic normality of the univariate components. We also establish the simultaneous confidence band for each of the univariate components. The performance of the proposed method is evaluated by two simulation studies. We apply the proposed method to analyze the crash counts data in the Tampa-St. Petersburg urbanized area in Florida.
|
