Nonparametric estimation of spacial data with kNN method

In this work we introduced a new estimator when the co-variables are functional in nature. This estimator is a mix of both the k Nearest Neighbors shortly (kNN) procedure and spacial functional data. Then the convergence rate are introduced when the considered sample is collected in spatial order with mixing structure.In theory there is an estimation of the risk point then a discussion of application difficulties, such as data driven bandwidth choice. Furthermore, a comparison study based on simulated and real data is also provided to illustratethe performances and the usefulness of the kNN approach and to prove the highly sensitive of the kNN approach to the presence of even a small proportion of outliers in the data.