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.
Citation
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
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