quantreg (version 4.77)

rq.fit.sfn: Sparse Regression Quantile Fitting

Description

Fit a quantile regression model using a sparse implementation of the Frisch-Newton interior-point algorithm.

Usage

rq.fit.sfn(a, y, tau = 0.5, rhs = (1-tau)*c(t(a) %*% rep(1,length(y))), control)

Arguments

a

structure of the design matrix X stored in csr format

y

response vector

tau

desired quantile

rhs

the right-hand-side of the dual problem; regular users shouldn't need to specify this, but in special cases can be quite usefully altered to meet special needs. See e.g. Section 6.8 of Koenker (2005).

control

control parameters for fitting routines: see sfn.control

Value

• coef
  Regression quantile coefficients
• ierr
  Error code for the internal Fortran routine srqfnc: [object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
• it
  Iteration count
• time
  Amount of time used in the computation

Details

This is a sparse implementation of the Frisch-Newton algorithm for quantile regression described in Portnoy and Koenker (1997). The sparse matrix linear algebra is implemented through the functions available in the R package SparseM.

References

Portnoy, S. and R. Koenker (1997) The Gaussian Hare and the Laplacean Tortoise: Computability of Squared-error vs Absolute Error Estimators, (with discussion). Statistical Science, 12, 279-300.

Koenker, R and Ng, P. (2003). SparseM: A Sparse Matrix Package for R, J. of Stat. Software, 8, 1--9.

Koenker, R. (2005) Quantile Regression, Cambridge U. Press.

See Also

rq.fit.sfnc for the constrained version, SparseM for a sparse matrix package for R

Examples

## An artificial example :
n <- 200
p <- 50
set.seed(101)
X <- rnorm(n*p)
X[abs(X) < 2.0] <- 0
X <- cbind(1, matrix(X, n, p))
y <- 0.5 * apply(X,1,sum) + rnorm(n) ## true beta = (0.5, 0.5, ...)

sX <- as.matrix.csr(X)
try(rq.o <- rq.fit.sfn(sX, y)) #-> not enough tmp memory
(tmpmax <- floor(1e5 + exp(-12.1)*(sX@ia[p+1]-1)^2.35))
## now ok:
rq.o <- rq.fit.sfn(sX, y, control = list(tmpmax= tmpmax))