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Strong uniform consistency of the local linear relative error regression estimator under left truncation

Author

Listed:
  • Feriel Bouhadjera

    (MISTEA, Université de Montpellier, INRAE, Montpellier SupAgro)

  • Mohamed Lemdani

    (Universié de Lille, Fac. Pharmacie, Lab. Biomaths METRICS)

  • Elias Ould Saïd

    (Université du Littoral Cote d’Opale (ULCO), Laboratoire de Mathématiques pures et appliquées (LMPA))

Abstract

This paper is concerned with a nonparametric estimator of the regression function based on the local linear method when the loss function is the mean squared relative error and the data left truncated. The proposed method avoids the problem of boundary effects and is robust against the presence of outliers. Under suitable assumptions, we establish the uniform almost sure strong consistency with a rate over a compact set. A simulation study is conducted to comfort our theoretical result. This is made according to different cases, sample sizes, rates of truncation, in presence of outliers and a comparison study is made with respect to classical, local linear and relative error estimators. Finally, an experimental prediction is given.

Suggested Citation

  • Feriel Bouhadjera & Mohamed Lemdani & Elias Ould Saïd, 2023. "Strong uniform consistency of the local linear relative error regression estimator under left truncation," Statistical Papers, Springer, vol. 64(2), pages 421-447, April.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01325-9
    DOI: 10.1007/s00362-022-01325-9
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    References listed on IDEAS

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    1. Wang, Jiang-Feng & Ma, Wei-Min & Fan, Guo-Liang & Wen, Li-Min, 2015. "Local linear quantile regression with truncated and dependent data," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 232-240.
    2. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    3. Elias Ould-Saïd & Mohamed Lemdani, 2006. "Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 357-378, June.
    4. Belkais Altendji & Jacques Demongeot & Ali Laksaci & Mustapha Rachdi, 2018. "Functional data analysis: estimation of the relative error in functional regression under random left-truncation model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(2), pages 472-490, April.
    5. Spierdijk, Laura, 2008. "Nonparametric conditional hazard rate estimation: A local linear approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2419-2434, January.
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