@article{Alshahrani2026, 
author = {Fatimah Alshahrani and Wahiba Bouabsa},
title = {Functional single-index    k-nearest neighbor relative error regression under weak dependence},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {19127-19161},
keywords = {functional single-index model, relative error regression, k-nearest neighbors, kernel estimator, almost complete convergence, quasi-associated dependence},
url = {https://www.sciopen.com/article/10.3934/math.2026779},
doi = {10.3934/math.2026779},
abstract = {We study estimation of the relative error regression function in a functional single-index regression model under quasi-associated dependence. We introduce a    k-nearest neighbors (   k-NN) estimator whose smoothing adapts to the local concentration of the covariate trajectories. Almost complete convergence rates are established under mild small-ball and dependence conditions. A simulation study compares the proposed    k-NN estimator with its kernel counterpart, and a real data application to air quality forecasting (NOx    → ozone) illustrates it's practical performance.}
}