  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 usual 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.
