SCADPenalized Quantile Regression
The fitting method implements the smoothly clipped absolute deviation
penalty of Fan and Li for fitting quantile regression models.
When the argument lambda
is a scalar the penalty function is the scad modified l1
norm of the last (p-1) coefficients, under the presumption that the
first coefficient is an intercept parameter that should not be subject
to the penalty. When lambda is a vector it should have length
equal the column dimension of the matrix x and then defines a
coordinatewise specific vector of scad penalty parameters. In this
case lambda entries of zero indicate covariates that are not
penalized. There should be a sparse version of this, but isn't (yet).
rq.fit.scad(x, y, tau = 0.5, alpha = 3.2, lambda = 1, start="rq", beta = .9995, eps = 1e-06)
x |
the design matrix |
y |
the response variable |
tau |
the quantile desired, defaults to 0.5. |
alpha |
tuning parameter of the scad penalty. |
lambda |
the value of the penalty parameter that determines how much shrinkage is done.
This should be either a scalar, or a vector of length equal to the column dimension
of the |
start |
starting method, default method 'rq' uses the unconstrained rq estimate, while method 'lasso' uses the corresponding lasso estimate with the specified lambda. |
beta |
step length parameter for Frisch-Newton method. |
eps |
tolerance parameter for convergence. |
The algorithm is an adaptation of the "difference convex algorithm" described in Wu and Liu (2008). It solves a sequence of (convex) QR problems to approximate solutions of the (non-convex) scad problem.
Returns a list with a coefficient, residual, tau and lambda components.
When called from "rq" as intended the returned object
has class "scadrqs".
R. Koenker
Wu, Y. and Y. Liu (2008) Variable Selection in Quantile Regression, Statistica Sinica, to appear.
n <- 60
p <- 7
rho <- .5
beta <- c(3,1.5,0,2,0,0,0)
R <- matrix(0,p,p)
for(i in 1:p){
for(j in 1:p){
R[i,j] <- rho^abs(i-j)
}
}
set.seed(1234)
x <- matrix(rnorm(n*p),n,p) %*% t(chol(R))
y <- x %*% beta + rnorm(n)
f <- rq(y ~ x, method="scad",lambda = 30)
g <- rq(y ~ x, method="scad", start = "lasso", lambda = 30)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.