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In this paper, we study the estimation of partially linear models for spatialdata distributed over complex domains. We use bivariate splines overtriangulations to represent the nonparametric component on an irregulartwo-dimensional domain. The proposed method is formulated as a constrainedminimization problem which does not require constructing finite elements orlocally supported basis functions. Thus, it allows an easier implementation ofpiecewise polynomial representations of various degrees and various smoothnessover an arbitrary triangulation. Moreover, the constrained minimization problemis converted into an unconstrained minimization via a QR decomposition of thesmoothness constraints, which allows for the development of a fast andefficient penalized least squares algorithm to fit the model. The estimators ofthe parameters are proved to be asymptotically normal under some regularityconditions. The estimator of the bivariate function is consistent, and its rateof convergence is also established. The proposed method enables us to constructconfidence intervals and permits inference for the parameters. The performanceof the estimators is evaluated by two simulation examples and by a real dataanalysis.

Efficient Estimation of Partially Linear Models for Spatial Data over Complex Domain