Asymptotic properties of a conditional quantile estimator with randomly truncated data

  • Authors:

  • Mohamed Lemdani;Elias Ould-Saïd;Nicolas Poulin

  • Affiliations:

  • Lab. de Biomathématiques, Univ. de Lille 2. Fac. de Pharmacie, 3, rue du Pr. Laguesse, 59006 Lille, France;L.M.P.A. J. Liouville, Univ. du Littoral Côte d'Opale, BP 699, 62228 Calais, France;L.M.P.A. J. Liouville, Univ. du Littoral Côte d'Opale, BP 699, 62228 Calais, France

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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Abstract

Let Y be a response variable that is subject to left-truncation by a variable T. We consider the problem of estimating its conditional quantile function given a vector of covariates X. We derive almost sure (a.s.) consistency and asymptotic normality results for a kernel estimate of the conditional quantile function. Simulations are drawn to illustrate the results for finite samples.