Conditional quantile sequential estimation for stochastic codes

Tatiana Labopin-Richard (1) , Fabrice Gamboa (1) , Aurélien Garivier (2, 3) , Jerome Stenger (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
3 MC2 - Modèles de calcul, Complexité, Combinatoire
4 EDF R&D - EDF R&D

We propose and analyze an algorithm for the sequential estimation of a conditional quantile in the context of real stochastic codes with vectorvalued 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.

Mots clés: stochastic code; quantile; non-asymptotic inequality; k nearest neighbors; stochastic algorithm

Domaines: Théorie [stat.TH]

Tatiana Labopin-Richard, Fabrice Gamboa, Aurélien Garivier, Jerome Stenger. Conditional quantile sequential estimation for stochastic codes. 2015. ⟨hal-01187329v7⟩