Local linear regression for functional data under quasi-associated dependence with fixed and $k$NN bandwidths

Local linear kernel estimation is a fundamental tool in nonparametric regression, renowned for its bias reduction and boundary correction properties. While its asymptotic behavior is well understood for independent data and for strongly mixing processes, it remains largely unexplored under quasi-associated dependence, even in the real-valued regression setting. In this paper, we introduce a functional local linear kernel estimator for regression models with quasi-associated observations. We establish strong consistency in the sense of almost complete convergence and derive convergence rates under mild regularity conditions involving small-ball probabilities and covariance decay. To the best of our knowledge, this paper provides the first theoretical guarantees for functional local linear kernel regression under quasi-associated dependence, covering both fixed and $k$-nearest neighbor ( $k$NN) bandwidth selection procedures.