astar_1, bstar_n {OrdMonReg}R Documentation

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, ..., 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 fadoua@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~fadoua

Kaspar Rufibach (maintainer) kaspar.rufibach@ifspm.uzh.ch
http://www.biostat.uzh.ch/aboutus/people/rufibach.html

Filippo Santambrogio filippo@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~filippo

References

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

See Also

This function is used by BoundedAntiMeanTwo.


[Package OrdMonReg version 1.0.0 Index]