Description: Method for develops a classification model for ordinal responses based on logic regression.

Title: Compute least squares estimates of one bounded or two ordered
Author: Fadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio
Description: We consider the problem of estimating two antitonic
regression curves f1* and f2* under the constraint that f1* >=
f2*. Given two sets of n data points g1(x_1), ..., g1(x_n) and
g2(x_1), ..., g2(x_n) that are observed at (the same)
deterministic points x_1, ..., x_n, the estimates are obtained
by minimizing the Least Squares criterion L(f1, f2) =
(g2(x_i) - f2(x_i))^2 w2(x_i) over the class of pairs of
functions (f1, f2) such that f1 and f2 are antitonic and
f1(x_i) >= f2(x_i) for all i = 1, ..., n. The estimates are
computed with a projected subgradient algorithm where the
Packaged: Tue Apr 14 20:39:09 2009; rufibach

Description: We consider the problem of estimating two isotonic
regression curves g1* and g2* under the constraint that they
are ordered, i.e. g1* <= g2*. Given two sets of n data points
y_1, ..., y_n and z_1, ..., z_n that are observed at (the same)
deterministic design points x_1, ..., x_n, the estimates are
obtained by minimizing the Least Squares criterion L(a, b) =
w2(x_i) over the class of pairs of vectors (a, b) such that a
and b are isotonic and a_i <= b_i for all i = 1, ..., n. The
estimates are computed with a projected subgradient algorithm
where the projection is calculated using a PAVA.

and b are isotonic and a_i <= b_i for all i = 1, ..., n. We
offer two different approaches to compute the estimates: a
projected subgradient algorithm where the projection is
calculated using a PAVA as well as Dykstra's cyclical

Description: We consider the problem of estimating two isotonic regression curves g1* and g2* under the constraint that they are ordered, i.e. g1* <= g2*. Given two sets of n data points y_1, ..., y_n and z_1, ..., z_n that are observed at (the same) deterministic design points x_1, ..., x_n, the estimates are obtained by minimizing the Least Squares criterion L(a, b) = sum_{i=1}^n (y_i - a_i)^2 w1(x_i) + sum_{i=1}^n (z_i - b_i)^2 w2(x_i) over the class of pairs of vectors (a, b) such that a and b are isotonic and a_i <= b_i for all i = 1, ..., n. We offer two different approaches to compute the estimates: a projected subgradient algorithm where the projection is calculated using a PAVA as well as Dykstra's cyclical projection algorithm.