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Behaviormetrika

, Volume 46, Issue 1, pp 199–233 | Cite as

Asymptotic normality of some conditional nonparametric functional parameters in high-dimensional statistics

  • Oussama Bouanani
  • Ali Laksaci
  • Mustapha RachdiEmail author
  • Saâdia Rahmani
Original Paper

Abstract

This paper deals with the convergence in distribution of estimators of some conditional parameters in the Functional Data Analysis framework. In fact, we consider models where the input is of functional kind and the output is a scalar. Then, we establish the asymptotic normality of the nonparametric local linear estimators of (1) the conditional distribution function and (2) the successive derivatives of the conditional density. Moreover, as by-product, we deduce the asymptotic normality of the local linear estimator of the conditional mode. Finally, to show interests of our results, on the practical point of view, we have conducted a computational study, first on a simulated data and, then on some real data concerning the forage quality.

Keywords

Functional data analysis (FDA) Local linear estimation Conditional cumulative distribution Derivatives of the conditional density Conditional mode Asymptotic normality Small ball probability Forage quality 

Mathematics Subject Classification

62G05 62G08 62G20 62G35 62G07 62G32 62G30 Secondary 62H12 

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Copyright information

© The Behaviormetric Society 2018

Authors and Affiliations

  1. 1.Laboratoire de Modèles Stochastiques, Statistique et ApplicationsUniversité Docteur Moulay TaherSaïdaAlgeria
  2. 2.Department of Mathematics, College of ScienceKing Khalid UniversityAbhaSaudi Arabia
  3. 3.Université Grenoble Alpes (France), Laboratoire AGEIS, EA 7407Grenoble Cedex 09France

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