astar_1, bstar_n: 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
$a_1^*$ and $b_n^*$ are returned.
References
Balabdaoui, F., Rufibach, K., Santambrogio, F. (2009).
Least squares estimation of two ordered monotone regression curves.
Preprint.