k ‐Nearest neighbors local linear regression for functional and missing data at random

We combine the k ‐Nearest Neighbors ( k NN) method to the local linear estimation (LLE) approach to construct a new estimator (LLE‐ k NN) of the regression operator when the regressor is of functional type and the response variable is a scalar but observed with some missing at random (MAR) observations. The resulting estimator inherits many of the advantages of both approaches ( k NN and LLE methods). This is confirmed by the established asymptotic results, in terms of the pointwise and uniform almost complete consistencies, and the precise convergence rates. In addition, a numerical study (i) on simulated data, then (ii) on a real dataset concerning the sugar quality using fluorescence data, were conducted. This practical study clearly shows the feasibility and the superiority of the LLE‐ k NN estimator compared to competitive estimators.