astar_1, bstar_n {OrdMonReg}

Computes explicitly known values of the estimates in the two ordered functions antitonic regression problem

Description

These functions compute the values a_1^* and b_n^*, the value of the estimate of the upper function at x_1 and the value of the lower estimated function at x_n in the two ordered antitonic regression functions problem. These values can be computed via explicit formulas, unlike the values at x \in {x_2, \ldots, x_{n-1}}, which are received via a projected subgradient algorithm. However, b_n^* enters this algorithm as an auxiliary quantity.

Usage

astar_1(g1, w1, g2, w2)
bstar_n(g1, w1, g2, w2)

Arguments

g1

Vector in R^n, measurements of upper function.

w1

Vector in R^n, weights for upper function.

g2

Vector in R^n, measurements of lower function.

w2

Vector in R^n, weights for lower function.

Value

Values of a_1^* and b_n^* are returned.

Author(s)

Fadoua Balabdaoui [e-mail]
http://www.ceremade.dauphine.fr/~fadoua

Kaspar Rufibach (maintainer) [e-mail]
http://www.kasparrufibach.ch

Filippo Santambrogio [e-mail]
http://www.math.u-psud.fr/~santambr/

References

Balabdaoui, F., Rufibach, K., Santambrogio, F. (2009). Least squares estimation of two ordered monotone regression curves. Preprint.

See Also

This function is used by BoundedAntiMeanTwo.