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...

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Bibliographic Details
Published in:	Journal of statistical theory and practice Vol. 13; no. 4
Main Authors:	Labopin-Richard, Tatiana, Gamboa, Fabrice, Garivier, Aurélien, Stenger, Jérôme
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-12-2019
Subjects:	Mathematics and Statistics Original Article Probability Theory and Stochastic Processes Statistical Theory and Methods Statistics 62L12 Conditional quantile Stochastic code Nearest neighbors method 62G32 Robbins–Monro stochastic algorithm 62L20
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Summary:	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.
ISSN:	1559-8608 1559-8616
DOI:	10.1007/s42519-019-0053-8