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Functional data analysis: local linear estimation of the \(L_1\)-conditional quantiles

  • Fahimah A. Al-Awadhi
  • Zoulikha Kaid
  • Ali Laksaci
  • Idir Ouassou
  • Mustapha Rachdi
Original Paper
  • 39 Downloads

Abstract

We consider a new estimator of the quantile function of a scalar response variable given a functional random variable. This new estimator is based on the \(L_1\) approach. Under standard assumptions, we prove the almost-complete consistency as well as the asymptotic normality of this estimator. This new approach is also illustrated through some simulated data and its superiority, compared to the classical method, has been proved for practical purposes.

Keywords

Functional data analysis (FDA) Small ball probability Local linear method (LLM) Conditional quantiles Asymptotic normality Almost-complete (a.co.) convergence 

Mathematics Subject Classification

62G08 62G10 62G35 62G07 62G32 62G30 Secondary 62H12 

Notes

Acknowledgements

The authors would like to thank the Associate-Editor and an anonymous reviewer for their valuable comments and suggestions which improved substantially the quality of this paper. The second and the third authors would like to express their gratitude to King Khalid University (Saudi Arabia) for providing administrative and technical supports.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Science Department of Statistics and Operations ResearchKuwait UniversitySafatKuwait
  2. 2.Department of Mathematics, College of ScienceKing Khalid UniversityAbhaSaudi Arabia
  3. 3.Ecole Nationale des Sciences AppliquéesUniversité Cadi AyyadMarrakechMorocco
  4. 4.University Mohammed VI PolytechniqueBen GuerirMorocco
  5. 5.TIMB Team, Laboratoire AGEIS EA 7407, UFR SHSUniversity Grenoble AlpesGrenoble Cedex 09France

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