Restricted Regression Quantiles

Regression quantiles can be used as prediction intervals for the response variable. But such applications are often hampered by the problem of quantile crossing in finite sample cases. This article examines the efficiency properties of restricted regression quantiles that are proposed by X. He (1997, Amer. Statist.51, 186–192) to overcome the crossing problem of the usual regression quantiles of R. Koenker and G. Bassett (1978, Econometrica46, 33–50) for linear models. An example using esterase assay data is presented to illustrate the use of restricted regression quantiles in constructing calibration intervals.