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December, 1992 Estimating Conditional Quantiles at the Root of a Regression Function
Hari Mukerjee
Ann. Statist. 20(4): 2168-2176 (December, 1992). DOI: 10.1214/aos/1176348911

Abstract

The Robbins-Monro process $X_{n+1} = X_n - c_n Y_n$ is a standard stochastic approximation method for estimating the root $\theta$ of an unknown regression function. There is a vast literature on the convergence properties of $X_n$ to $\theta$. In practice, one is also interested in the conditional distribution of the system under the sequential control when the control is set at $\theta$ or near $\theta$. This problem appears to have received no attention in the literature. We introduce an estimator using methods of nonparametric conditional quantile estimation and derive its asymptotic properties.

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Hari Mukerjee. "Estimating Conditional Quantiles at the Root of a Regression Function." Ann. Statist. 20 (4) 2168 - 2176, December, 1992. https://doi.org/10.1214/aos/1176348911

Information

Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0783.62059
MathSciNet: MR1193334
Digital Object Identifier: 10.1214/aos/1176348911

Subjects:
Primary: 62G05
Secondary: 60F05, 60F15, 62L20

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 4 • December, 1992
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