The k-nearest neighbors method in single index regression model for functional quasi-associated time series data

In the present paper, we consider the k-Nearest Neighbors (k-NN) method in the single index regression model in the case of a functional predictor and a scalar response. The main result of this work is the establishment of the almost complete convergence rates for the quasi-associated data. The obtained results rely on the classical functional kernel estimate. Some simulation studies are carried out to show the finite sample performances of the k-NN estimator. Finally, we show how to use the k-NN estimator of the functional single index regression model in the analysis of air quality to illustrate the effectiveness of our methodology.