Uniform bias study and Bahadur representation for local polynomial estimators of the conditional quantile function

This paper investigates the bias and the Bahadur representation of a local poly-nomial estimator of the conditional quantile function and its derivatives. Thebias and Bahadur remainder term are studied uniformly with respect to thequantile level, the covariates and the smoothing parameter. The order of thelocal polynomial estimator can be higher that the differentiability order of theconditional quantile function. Applications of the results deal with global opti-mal consistency rates of the local polynomial quantile estimator, performanceof random bandwidths and estimation of the conditional quantile density func-tion. The latter allows to obtain a simple estimator of the conditional quantilefunction of the private values in a first price sealed bids auctions under theindependent private values paradigm and risk neutrality. JEL Classification: Primary C14; Secondary C21.