Sankhya A

, Volume 73, Issue 1, pp 125–141 | Cite as

Asymptotic results for an L1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology

Article

Abstract

In this paper, we study an L1-norm kernel estimator of the conditional quan- tile (CQ) of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. The almost complete (a.co.) consis- tency and the asymptotic normality of this estimate are obtained when the sample is an α-mixing sequence. We illustrate our methodology by applying the estimator to climatological data.

Keywords and phrases

Asymptotic distribution dependency functional data robust estimation 

AMS (2000) subject classification

Primary 62G20 Secondary 62G08, 62G35, 62E20 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bradley, R.C. (2007). Introduction to strong mixing conditions. Vol. I–III. Kendrick Press, Utah.Google Scholar
  2. Doukhan, P., Massart, P. and Rio, E. (1994). The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincar Probab. Statist., 30, 63–82.MathSciNetMATHGoogle Scholar
  3. Ezzahrioui, M. and Ould Saïd, E. (2008). Asymptotic results of a nonparametric conditional quantile estimator for functional time series data. Comm. Statist. Theory Methods. 37, 2735–2759.MathSciNetMATHCrossRefGoogle Scholar
  4. Ferraty, F., Laksaci, A., Tadj, A. and Vieu, P. (2009). Rate of uniform consistency for nonparametric estimates with functional variables. J. Statist. Plann. Inference, 140, 335–352.MathSciNetCrossRefGoogle Scholar
  5. Ferraty, F., Mas, A. and Vieu, P. (2007). Nonparametric regression on functional data: inference and practical aspects. Aust. N. Z. J. Stat., 49, 267–286.MathSciNetMATHCrossRefGoogle Scholar
  6. Ferraty, F., Rabhi, A. and Vieu, P. (2005). Conditional quantiles for functional dependent data with application to the climatic El Niño phenomenon. Sankhyā, 67, 378–398.MathSciNetMATHGoogle Scholar
  7. Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis. Theory and Practice. Springer-Verlag, New York.MATHGoogle Scholar
  8. Gannoun, A., Saracco, J. and Yu, K. (2003). Nonparametric prediction by conditional median and quantiles. J. Statist. Plann. Inference, 117, 207–223.MathSciNetMATHCrossRefGoogle Scholar
  9. Laksaci, A., Lemdani, M. and Ould Saïd, E. (2009). L 1-norm kernel estimator of conditional quantile for functional regressors: consistency and asymptotic normality. Statist. Probab. Lett., 79, 1065–1073.MathSciNetMATHCrossRefGoogle Scholar
  10. Lin, Z. and Li, D. (2007). Asymptotic normality for L 1-norm kernel estimator of conditional median under association dependence. J. Multivariate Anal., 98, 1214–1230.MathSciNetMATHCrossRefGoogle Scholar
  11. Masry, E. (1986). Recursive probability density estimation for weakly dependent stationary processus. IEEE Trans. Inform. Theory, 32, 254–267.MathSciNetMATHCrossRefGoogle Scholar
  12. Polonik, W. and Yao, Q. (2000). Conditional minimum volume predictive regions for stochastic processes. J. Amer. Statist. Assoc., 95, 509–519.MathSciNetMATHCrossRefGoogle Scholar
  13. Rio, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants (in French). Mathématiques et Applications, 31. Springer, Berlin.MATHGoogle Scholar

Copyright information

© Indian Statistical Institute 2011

Authors and Affiliations

  • Ali Laksaci
    • 1
    • 4
  • Mohamed Lemdani
    • 2
    • 5
  • Elias Ould Saïd
    • 3
    • 6
    • 7
  1. 1.Univ. Djillali LiabèsSidi Bel AbbèsAlgeria
  2. 2.Univ. de Lille 2LilleFrance
  3. 3.Univ. du Littoral Côte d’OpaleCalaisFrance
  4. 4.Dép. de MathématiquesUniv. D. LiabèsLiabèsAlgeria
  5. 5.Lab. Biomaths.Univ. de Lille 2, Fac. PharmacieLilleFrance
  6. 6.Univ. Lille Nord de FranceLilleFrance
  7. 7.U.L.C.O., L.M.P.A.CalaisFrance

Personalised recommendations