AISM 52, 459-470

Nonparametric estimation of a conditional quantile
for alpha-mixing processes

Toshio Honda

Institute of Social Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

(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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