Restricted regression quantiles

Regression quantiles can be used as prediction intervals for the response V ariable. But such applications are often hampered by the problem of quantil e crossing in finite sample cases. This article examines the efficiency pro perties of restricted regression quantiles that are proposed by X. He (1997 , Amer. Statist.51.186-192) to overcome the crossing problem of the usual r egression quantiles of R. Koenker and G. Bassett (1978. Econometrica 46 . 3 3-50) for linear models. An example using esterase assay data is presented to illustrate the use of restricted regression quantiles in constructing ca libration intervals. (C) 2000 Academic Press AMS 1991 subject classificatio ns: 62J05.