Strong uniform consistency of the local linear relative error regression estimator under left truncation - INRAE - Institut national de recherche pour l’agriculture, l’alimentation et l’environnement
Article Dans Une Revue Statistical Papers Année : 2023

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

Résumé

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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Dates et versions

hal-03699621 , version 1 (20-06-2022)

Identifiants

Citer

Feriel Bouhadjera, Mohamed Lemdani, Elias Ould Saïd. Strong uniform consistency of the local linear relative error regression estimator under left truncation. Statistical Papers, 2023, 64 (2), pp.421-447. ⟨10.1007/s00362-022-01325-9⟩. ⟨hal-03699621⟩
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