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

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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.

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Acknowledgements

The authors are grateful to two anonymous referees whose careful reading gave them the opportunity to improve the quality of the paper by addressing the theoretical issue of dependency and enriching the simulation part.

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Authors and Affiliations

  1. MISTEA, Université de Montpellier, INRAE, Montpellier SupAgro, Montpellier, France

    Feriel Bouhadjera

  2. Universié de Lille, Fac. Pharmacie, Lab. Biomaths METRICS, 59006, Lille, France

    Mohamed Lemdani

  3. Université du Littoral Cote d’Opale (ULCO), Laboratoire de Mathématiques pures et appliquées (LMPA), 50 rue Ferdinand Buisson, 62100, Calais, France

    Elias Ould Saïd

Authors
  1. Feriel Bouhadjera
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  2. Mohamed Lemdani
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  3. Elias Ould Saïd
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Correspondence to Mohamed Lemdani.

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Bouhadjera, F., Lemdani, M. & Ould Saïd, E. Strong uniform consistency of the local linear relative error regression estimator under left truncation. Stat Papers 64, 421–447 (2023). https://doi.org/10.1007/s00362-022-01325-9

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  • DOI: https://doi.org/10.1007/s00362-022-01325-9

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