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Asymptotic normality of the relative error regression function estimator for censored and time series data

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  • Bouhadjera Feriel

    (Université Badji-Mokhtar, Lab. de Probabilités et Statistique. BP 12, 23000 Annaba, Algérie. Université du Littoral Côte d’Opale. Lab. de Math. Pures et Appliquées. 50 Rue Ferdinand Buisson, 62100, Calais, France.)

  • Saïd Elias Ould

    (Université du Littoral Côte d’Opale. Lab. de Math. Pures et Appliquées. IUT de Calais. 19, rue Louis David. 62228, Calais, France.)

Abstract

Consider a survival time study, where a sequence of possibly censored failure times is observed with d-dimensional covariate The main goal of this article is to establish the asymptotic normality of the kernel estimator of the relative error regression function when the data exhibit some kind of dependency. The asymptotic variance is explicitly given. Some simulations are drawn to lend further support to our theoretical result and illustrate the good accuracy of the studied method. Furthermore, a real data example is treated to show the good quality of the prediction and that the true data are well inside in the confidence intervals.

Suggested Citation

  • Bouhadjera Feriel & Saïd Elias Ould, 2021. "Asymptotic normality of the relative error regression function estimator for censored and time series data," Dependence Modeling, De Gruyter, vol. 9(1), pages 156-178, January.
    • Handle: RePEc:vrs:demode:v:9:y:2021:i:1:p:156-178:n:5
    DOI: 10.1515/demo-2021-0107
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    References listed on IDEAS

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    1. Anouar El Ghouch & Ingrid Van Keilegom, 2008. "Non‐parametric Regression with Dependent Censored Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(2), pages 228-247, June.
    2. Park, Heungsun & Stefanski, L. A., 1998. "Relative-error prediction," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 227-236, October.
    3. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
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