Functional data analysis: estimation of the relative error in functional regression under random left-truncation model

• Published in: Journal of nonparametric statistics Vol. 30; no. 2; pp. 472 - 490
• Main Authors: Altendji, Belkais, Demongeot, Jacques, Laksaci, Ali, Rachdi, Mustapha
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Ltd 03.04.2018; American Statistical Association
• Subjects: Computer simulation; Data analysis; Error analysis; Estimating techniques; Mathematics; Normality; Random variables; Regression analysis; Regression models; Statistics; Well construction
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485252.2018.1438609

In this paper, we investigate the relationship between a functional random covariable and a scalar response which is subject to left-truncation by another random variable. Precisely, we use the mean squared relative error as a loss function to construct a nonparametric estimator of the regression operator of these functional truncated data. Under some standard assumptions in functional data analysis, we establish the almost sure consistency, with rates, of the constructed estimator as well as its asymptotic normality. Then, a simulation study, on finite-sized samples, was carried out in order to show the efficiency of our estimation procedure and to highlight its superiority over the classical kernel estimation, for different levels of simulated truncated data.