Functional Nonparametric Estimation of a Conditional Distribution Function under Spatial Weak Dependence

This paper addresses the asymptotic analysis of a nonparametric kernel estimator for conditional distribution functions in the context of spatially weakly dependent functional variables, where the covariates lie in an infinite-dimensional space. We focus on establishing the almost complete convergence (a.~co) of the estimator and deriving its rate of convergence under a spatial sampling framework characterized by quasi-association. By integrating spatial structure into the theoretical development, we highlight the impact of weak spatial dependence on the performance of the estimator. Our results provide key insights into the applicability and robustness of kernel-based nonparametric inference for spatially structured functional data.