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