NONPARAMETRIC ESTIMATION OF A CONDITIONAL QUANTILE FOR α-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 (X′_{i}, Y_{i})′ be a set of observations form a stationary α-mixing process and θ(x) be the conditional α-th quantile of Y given X = x. Several authors considered nonparametric estimation of θ(x) in the i.i.d. setting. Assuming the smoothness of θ(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, α-mixing process, exponential inequality, Bahadur representation, uniform convergence.