pSolver function

Quantile Regression

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

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.

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.

Returns

• x: Vector containing the fitted values

• lbd: Vector with Lagrange multipliers

• f: Value of the target function

• gx: Gradient at point x

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)