Bootstrap method exploiting preprocessing strategy to reduce
computation time for large problem. In contrast to
boot.rq.pxy which uses the classical multinomial
sampling scheme and is coded in R, this uses the exponentially
weighted bootstrap scheme and is coded in fortran and consequently
is considerably faster in larger problems.
boot.rq.pwxy(x, y, tau, coef, R = 200, m0 = NULL, eps = 1e-06, ...)returns a list with elements:
a matrix of dimension ncol(x) by R
a 5 by m matrix of iteration counts
an m-vector of convergence flags
Design matrix
response vector
quantile of interest
point estimate of fitted object
the number of bootstrap replications desired.
constant to determine initial sample size, defaults to sqrt(n*p) but could use some further tuning...
tolerance for convergence of fitting algorithm
other parameters not yet envisaged.
Blaise Melly and Roger Koenker
The fortran implementation is quite similar to the R code for
boot.rq.pxy except that there is no multinomial sampling.
Instead rexp(n) weights are used.
Chernozhukov, V. I. Fernandez-Val and B. Melly, Fast Algorithms for the Quantile Regression Process, 2019, arXiv, 1909.05782,
Portnoy, S. and R. Koenker, The Gaussian Hare and the Laplacian Tortoise, Statistical Science, (1997) 279-300
boot.rq.pxy