Conditional Quantile Sequential Estimation for Stochastic Codes

  • Tatiana Labopin-Richard
  • Fabrice Gamboa
  • Aurélien GarivierEmail author
  • Jérôme Stenger
Original Article


We propose and analyze an algorithm for the sequential estimation of a conditional quantile in the context of real stochastic codes with vector-valued inputs. Our algorithm is based on k-nearest neighbors smoothing within a Robbins–Monro estimator. We discuss the convergence of the algorithm under some conditions on the stochastic code. We provide non-asymptotic rates of convergence of the mean squared error, and we discuss the tuning of the algorithm’s parameters.


Stochastic code Conditional quantile Robbins–Monro stochastic algorithm k-Nearest neighbors method 

Mathematics Subject Classification

62L12 62L20 62G32 



On behalf of all authors, the corresponding author states that there is no conflict of interest. Aurélien Garivier acknowledges the support of the Project IDEXLYON of the University of Lyon, in the framework of the Programme Investissements d’Avenir (ANR-16-IDEX-0005).


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Copyright information

© Grace Scientific Publishing 2019

Authors and Affiliations

  1. 1.Institut de Mathématique de ToulouseUniversité Paul SabatierToulouseFrance
  2. 2.Unité de Mathématiques Pures et Appliquées, Laboratoire de l’Informatique du ParallélismeÉcole Normale Supérieure de Lyon, Université de LyonLyonFrance
  3. 3.EDF R&DChatouFrance

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