Conditional quantile sequential estimation for stochastic codes

TL;DR

This paper introduces a sequential estimation algorithm for conditional quantiles in stochastic codes with vector inputs, combining k-nearest neighbors smoothing and Robbins-Monro, with convergence analysis and convergence rate results.

Contribution

The paper presents a novel algorithm that integrates k-nearest neighbors with Robbins-Monro for conditional quantile estimation in stochastic codes, including convergence and rate analysis.

Findings

Convergence of the proposed algorithm under certain conditions.

Non-asymptotic mean squared error rates established.

Guidelines for tuning algorithm parameters provided.

Abstract

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.