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

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 op...

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Published inJournal of nonparametric statistics Vol. 30; no. 2; pp. 472 - 490
Main Authors Altendji, Belkais, Demongeot, Jacques, Laksaci, Ali, Rachdi, Mustapha
Format Journal Article
LanguageEnglish
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
Online AccessGet full text
ISSN1048-5252
1029-0311
DOI10.1080/10485252.2018.1438609

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Abstract 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.
AbstractList 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.
Author Laksaci, Ali
Rachdi, Mustapha
Demongeot, Jacques
Altendji, Belkais
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  fullname: Rachdi, Mustapha
  organization: UFR SHS, Univ. Grenoble-Alpes, Equipe AGIM, Laboratoire AGEIS EA 7407, Université Grenoble-Alpes, Grenoble Cedex 09, France
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Snippet In this paper, we investigate the relationship between a functional random covariable and a scalar response which is subject to left-truncation by another...
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SubjectTerms Computer simulation
Data analysis
Error analysis
Estimating techniques
Mathematics
Normality
Random variables
Regression analysis
Regression models
Statistics
Well construction
Title Functional data analysis: estimation of the relative error in functional regression under random left-truncation model
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