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On the Strong Consistency of the Kernel Estimator of Extreme Conditional Quantiles

  • Stéphane Girard
  • Sana Louhichi
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Nonparametric regression quantiles can be obtained by inverting a kernel estimator of the conditional distribution. The asymptotic properties of this estimator are well known in the case of ordinary quantiles of fixed order. The goal of this paper is to establish the strong consistency of the estimator in case of extreme conditional quantiles. In such a case, the probability of exceeding the quantile tends to zero as the sample size increases, and the extreme conditional quantile is thus located in the distribution tails.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.MistisInria Grenoble Rhône-Alpes and Laboratoire Jean KuntzmannGrenobleFrance
  2. 2.Laboratoire Jean KuntzmannUniv. Grenoble-AlpesSaint-Martin-d’HèresFrance

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