isotone (version 1.0-1)

pSolver: Quantile Regression

Description

Solver for the general p-quantile monotone regression problem with optional weights.

Usage

pSolver(z, a, extra)

Arguments

z

Vector containing observed response

a

Matrix with active constraints

extra

List with element y containing the observed response vector, weights with optional observation weights, aw and bw as quantile weights.

Value

• x
  Vector containing the fitted values
• lbd
  Vector with Lagrange multipliers
• f
  Value of the target function
• gx
  Gradient at point x

Details

This function is called internally in activeSet by setting mySolver = pSolver. Note that if aw = bw, we get the weighted median and therefore we solved the weighted absolute norm.

References

Koenker, R. (2005). Quantile regression. Cambridge, MA: Cambridge University Press.

See Also

activeSet

Examples

##Fitting quantile regression
set.seed(12345)
y <- rnorm(9)              ##response values
w <- rep(1,9)              ##unit weights
btota <- cbind(1:8, 2:9)   ##Matrix defining isotonicity (total order)
fit.p <- activeSet(btota, pSolver, weights = w, y = y, aw = 0.3, bw = 0.7)