Comparisons of Two Quantile Regression Smoothers

Abstract

The paper compares the small-sample properties of two non-parametric quantile regression estimators. The first is based on constrained B-spline smoothing (COBS) and the other is based on a variation and slight extension of a running interval smoother, which apparently has not been studied via simulations. The motivation for this paper stems from the Well Elderly 2 study, a portion of which was aimed at understanding the association between the cortisol awakening response and two measures of stress. COBS indicated what appeared be an unusual form of curvature. The modified running interval smoother gave a strikingly different estimate, which raised the issue of how it compares to COBS in terms of mean squared error and bias as well as its ability to avoid a spurious indication of curvature. R functions for applying the methods were used in conjunction with default settings for the various optional arguments. The results indicate that the modified running interval smoother has practical value. Manipulation of the optional arguments might impact the relative merits of the two methods, but the extent to which this is the case remains unknown.