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.
Publié le : 1992-12-14
Classification:
Conditional quantile,
Bahadur representation,
stochastic approximation,
Robbins-Monro process,
central limit theorem,
law of the iterated logarithm,
62G05,
62L20,
60F05,
60F15
@article{1176348911,
author = {Mukerjee, Hari},
title = {Estimating Conditional Quantiles at the Root of a Regression Function},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 2168-2176},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348911}
}
Mukerjee, Hari. Estimating Conditional Quantiles at the Root of a Regression Function. Ann. Statist., Tome 20 (1992) no. 1, pp. 2168-2176. http://gdmltest.u-ga.fr/item/1176348911/