Conditional quantile sequential estimation for stochastic codes

Date: 
February, 2016
Arxiv Number: 
1508.06505
Hal Number: 
01187329
Abstract: 
This paper is devoted to the estimation of conditional quantile, more precisely the quantile of the output of a real stochastic code whose inputs are in R d. In this purpose, we introduce a stochastic algorithm based on Robbins-Monro algorithm and on k-nearest neighbors theory. We propose conditions on the code for that algorithm to be convergent and study the non-asymptotic rate of convergence of the means square error. Finally, we give optimal parameters of the algorithm to obtain the best rate of convergence.