@article{article_1640600, title={Spatial $k$NN-Local linear estimation for semi-functional partial linear regression}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={54}, pages={1164–1186}, year={2025}, DOI={10.15672/hujms.1640600}, author={Baouche, Mohamed El Ouard and Tawfik, Benchikh and Fetitah, Omar and Guendouzi, Toufik}, keywords={Asymptotic normality, functional data analysis, {\it k}NN estimation, local linear estimation, partial linear regression}, abstract={The objective of this paper is to investigate a semi-functional partial linear regression model for spatial data. The estimators are constructed using a $k$-nearest neighbors local linear method.Then, under suitable regularity conditions, we establish the asymptotic distribution of the parametric component and derive the uniform almost sure convergence rate for the nonparametric component. To assess the performance of the proposed estimators, we performed both simulation studies and real-data analyses. The results are compared with existing methods for semi-functional partial linear regression models using cross-validation. Specifically, we evaluate the predictive performance in terms of mean squared error and compare it against several benchmark estimators, including the kernel estimator, the local linear estimator and the $k$NN estimator. This practical study clearly demonstrates the feasibility and superiority of the local linear method estimator $k$-nearest neighbors over competing methods. This is evidenced by the lower mean squared error achieved by this estimator in both the simulation study and the real data application. These results indicate that this hybrid approach effectively addresses the common issue of bandwidth selection and yields estimators with reduced bias.}, number={3}, publisher={Hacettepe University}, organization={This research was funded by Thematic Research Agency in Science and Technology (ATRST) for funding this work through research groups program under the project number PRFU, C00L03UN220120220002.}