Conditional Quantile Sequential Estimation for Stochastic Codes

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.