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

Mustapha Rachdi, Ali Laksaci, Zoulikha Kaid, Abbassia Benchiha and Fahimah A. Al‐Awadhi

Statistica Neerlandica, 2021, vol. 75, issue 1, 42-65

Abstract: We combine the k‐Nearest Neighbors (kNN) method to the local linear estimation (LLE) approach to construct a new estimator (LLE‐kNN) 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 (kNN 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‐kNN estimator compared to competitive estimators.

Date: 2021
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https://doi.org/10.1111/stan.12224

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