AISM 52, 459-470
(Received August 5, 1997; revised March 23, 1999)
Abstract. Let (Xi', Yi)' be a set of observations form a stationary alpha-mixing process and theta(x) be the conditional alpha-th quantile of Y given X=x. Several authors considered nonparametric estimation of theta(x) in the i.i.d. setting. Assuming the smoothness of theta(x), we estimate it by local polynomial fitting and prove the asymptotic normality and the uniform convergence.
Key words and phrases: Conditional quantile, local polynomial fitting, alpha-mixing process, exponential inequality, Bahadur representation, uniform convergence.
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