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Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology

Abstract

In this paper, we study an L 1-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.

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Correspondence to Ali Laksaci.

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Laksaci, A., Lemdani, M. & Saïd, E.O. Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology. Sankhya A 73, 125–141 (2011). https://doi.org/10.1007/s13171-011-0002-4

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  • DOI: https://doi.org/10.1007/s13171-011-0002-4

AMS (2000) subject classification

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

Keywords and phrases

  • Asymptotic distribution
  • dependency
  • functional data
  • robust estimation