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k ‐Nearest neighbors local linear regression for functional and missing data at random
Author(s) -
Rachdi Mustapha,
Laksaci Ali,
Kaid Zoulikha,
Benchiha Abbassia,
AlAwadhi Fahimah A.
Publication year - 2021
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12224
Subject(s) - estimator , pointwise , mathematics , missing data , linear regression , statistics , mathematical analysis
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.