[R] Robust variance estimation with rq (failure of the bootstrap?)

[James Shaw]

I am fitting quantile regression models using data collected from a
sample of 124 patients.  When modeling cross-sectional associations, I
have noticed that nonparametric bootstrap estimates of the variances
of parameter estimates are much greater in magnitude than the
empirical Huber estimates derived using summary.rq's "nid" option.
The outcome variable is severely skewed, and I am afraid that this may
be affecting the consistency of the bootstrap variance estimates.  I
have read that the m out of n bootstrap can be used to overcome this
problem.  However, this procedure requires both the original sample
(n) and the subsample (m) sizes to be large.  The version implemented
in rq.boot does not appear to provide any improvement over the naive
bootstrap.  Ultimately, I am interested in using median regression to
model changes in the outcome variable over time.  Summary.rq's robust
variance estimator is not applicable to repeated-measures data.  I
question whether the block (cluster) bootstrap variance estimator,
which can accommodate intraclass correlation, would perform well.  Can
anyone suggest alternatives for variance estimation in this situation?

Regards,

Jim


James W. Shaw, Ph.D., Pharm.D., M.P.H.
Assistant Professor
Department of Pharmacy Administration
College of Pharmacy
University of Illinois at Chicago
833 South Wood Street, M/C 871, Room 266
Chicago, IL 60612
Tel.: 312-355-5666
Fax: 312-996-0868
Mobile Tel.: 215-852-3045