QUANTILE CURVES WITHOUT CROSSING

Conventional regression techniques focus on the conditional averages, but often of more interest are lower or upper conditional quantiles. A more informative description of the relationship among variables can be obtained through regression quantiles (RQ). The percentile curves a re usually computed one level at a time, Associated with great flexibi lity is the embarrassing phenomenon of quantile crossing. We propose a restricted version of regression quantiles (RRQ) that avoids the occu rrence of crossing while maintaining sufficient modeling flexibility. RRQ remains in the general framework of the regression quantiles both conceptually and computationally. Because it relates all quantile func tions through the conditional median, it also means substantial saving s in computation costs when multiple quantiles for high-dimensional da ta are needed. Two examples in connection with the physical and engine ering sciences are presented to demonstrate the usefulness of RRQ curv es.