Non-crossing nonparametric estimates of quantile curves

Abstract

In this paper a new nonparametric estimate of conditional quantiles is proposed, that avoids the problem of crossing quantile curves [calculated for various p ist Element von (0; 1)]: The method uses an initial estimate of the conditional distribution function in a first step and solves the problem of inversion and monotonization with respect to p ist Element von (0; 1) simultaneously. It is demonstrated that the new estimates are asymptotically normal distributed and asymptotically first order equivalent to quantile estimates obtained by local constant or local linear smoothing of the conditional distribution function. The performance of the new procedure is illustrated by means of a simulation study and some comparisons with the currently available procedures which are similar in spirit with the proposed method are presented.