ESTIMATING CONDITIONAL QUANTILES AT THE ROOT OF A REGRESSION FUNCTION
成果类型：
Article
署名作者：
MUKERJEE, H
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348911
发表日期：
1992
页码：
2168-2176
关键词：
摘要：
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.