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

Feriel Bouhadjera (), Mohamed Lemdani () and Elias Ould Saïd ()
Additional contact information
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)

Statistical Papers, 2023, vol. 64, issue 2, No 3, 447 pages

Abstract: 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.

Keywords: Left truncated data; Local linear fit; Rate of consistency; Regression function; Relative error; Uniform almost sure consistency (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-022-01325-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01325-9

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-022-01325-9

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().