1\name{rq.fit.ppro}
2\alias{rq.fit.ppro}
3\title{
4    Preprocessing fitting method for QR
5}
6\description{
7    Preprocessing method for fitting quantile regression models that
8    exploits the fact that adjacent tau's should have nearly the same
9    sign vectors for residuals.
10}
11\usage{
12rq.fit.ppro(x, y, tau, weights = NULL, Mm.factor = 0.8, eps = 1e-06, ...)
13}
14\arguments{
15  \item{x}{
16      Design matrix
17}
18  \item{y}{
19      Response vector
20}
21  \item{tau}{
22      quantile vector of interest
23}
24  \item{weights}{
25      case weights
26}
27  \item{Mm.factor}{
28      constant determining initial sample size
29}
30  \item{eps}{
31      Convergence tolerance
32}
33  \item{\dots}{
34      Other arguments
35}
36}
37\details{
38    See references for further details.
39}
40\value{
41    Returns a list with components:
42    \item{coefficients}{Matrix of coefficient estimates}
43    \item{residuals}{Matrix of residual estimates}
44    \item{rho}{vector of objective function values}
45    \item{weights}{vector of case weights}
46}
47\references{
48     Chernozhukov, V.  I. Fernandez-Val and B. Melly,
49	Fast Algorithms for the Quantile Regression Process, 2020,
50	Empirical Economics.,
51
52     Portnoy, S.  and R. Koenker, The Gaussian Hare and the Laplacian
53	Tortoise, Statistical Science, (1997) 279-300
54}
55\author{
56    Blaise Melly and Roger Koenker
57}
58\seealso{
59\code{\link{rq.fit.pfn}}, \code{\link{boot.rq.pxy}}
60}
61\keyword{regression}
62