aSolver function

Asymmetric Least Squares

Minimizes Efron's asymmetric least squares regression.

aSolver(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, weight aw for y > x, and weight bw for y <= x

Details

This function is called internally in activeSet by setting mySolver = aSolver.

Returns

• x: Vector containing the fitted values

• lbd: Vector with Lagrange multipliers

• f: Value of the target function

• gx: Gradient at point x

References

Efron, B. (1991). Regression percentiles using asymmetric squared error loss. Statistica Sinica, 1, 93-125.

See Also

activeSet

Examples

##Fitting isotone regression using active set
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.asy <- activeSet(btota, aSolver, weights = w, y = y, aw = 0.3, bw = 0.5)