Strong convergence of a nonparametric relative error regression estimator under missing data with functional predictors

• Published in: Journal of the Korean Statistical Society Vol. 53; no. 4; pp. 970 - 1002
• Main Authors: Boucetta, Adel, Guessoum, Zohra, Ould-Said, Elias
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.12.2024; 한국통계학회
• Subjects: Applied Statistics; Bayesian Inference; Mathematics and Statistics; Research Article; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; 통계학; Censored data; Truncated data; 62G08; Functional data; Functional regression; 62G20; Relative error
• ISSN: 1226-3192; 2005-2863
• DOI: 10.1007/s42952-024-00275-2

In this paper, we develop a nonparametric estimator of the regression function for a functional explanatory variable and a scalar response variable that is subject to left truncation and right censoring. The estimator is constructed by minimizing the mean squared relative error, which is a robust criterion that reduces the impact of outliers relatively to the Nadaraya Watson estimator. We prove the pointwise and uniform convergence of the estimator under some regular conditions and assess its performance by a numerical study. We also investigate the robustness of the estimator using the influence function as a measure of sensitivity to outliers and apply the estimator to a real dataset.