OrdMonReg: Compute least squares estimates of one bounded or two ordered isotonic regression curves

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.

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AuthorFadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio
Date of publication2011-12-01 08:00:09
MaintainerKaspar Rufibach <kaspar.rufibach@gmail.com>
LicenseGPL (>= 2)
http://www.ceremade.dauphine.fr/~fadoua, http://www.kasparrufibach.ch, http://www.math.u-psud.fr/~santambr/

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