What ensures that the tau-th quantile of the residuals is (nearly) zero, is that there IS an intercept in the model, this is one of the conditions required for the subgradient to contain 0 provided there is an intercept, when there is no intercept there is constraint to enforce this any more.
url: www.econ.uiuc.edu/~roger Roger Koenker email rkoen...@uiuc.edu Department of Economics vox: 217-333-4558 University of Illinois fax: 217-244-6678 Urbana, IL 61801 > On Feb 24, 2017, at 5:10 AM, Helio Santana <helio.santana.1...@gmail.com> > wrote: > > Dear R community, > > I am a beginner in quantile regression and I have a question about a > specific problem. I have used the quantreg package to fit a QR with > inequality constrains: > > n <- 100 > p <- 5 > X <- matrix(rnorm(n*p),n,p) > y <- 0.95*apply(X,1,sum)+rnorm(n) > R <- cbind(0,rbind(diag(p),-diag(p))) > r <- c(rep(0,p),-rep(1,p)) > model <- rq(y~X,R=R,r=r,method="fnc") > > So, > >> quantile(model$residuals,0.5) >> -6.68836e-11 (It should be close to 0) > > > However, if I try to impose no intercept in the last problem: > > R <- cbind(0,rbind(diag(p),-diag(p))) > R <- R[,2:dim(R)[2]] > r <- c(rep(0,p),-rep(1,p)) > model <- rq(y~X-1,R=R,r=r,method="fnc") > > I obtain: > >> quantile(model$residuals,0.5) >> -0.03465427 > > As you can see, this quantile value is not close to 0 as I expected. Have I > an error in the formulation of the QR? > > Is it possible to fit a QR with inequality constrains and no intercept? > > Is there another alternative for solving this kind of problem? > > I would appreciate your comments. > > Best regards, > > Helio > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
