Asymptotic results of semi-functional partial linear regression estimate under functional spatial dependency

In this paper, we study the semi-functional partial linear regression for spatial data with considering a both parametric and nonparametric modeling. In this case we obtain the asymptotic normality of the parametric component, and probability convergence with rate of the nonparametric component under spatial dependency. Finally, the performance of the parametric and nonparametric estimators, for finite spatial sample sizes, are given by using simulated and real data with comparison to the nonparametric kernel regression (FNR) model by using cross-validation and k nearest neighbor methods.