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.


OrdMonReg_1.0.3 (2011/11/30)

  • added NAMESPACE
  • updated KRs and FSs contact details

OrdMonReg_1.0.2 (2009/10/15)

  • corrected function 'boundedAntiMeanTwo.R'
  • added function 'boundedIsoMeanTwoDykstra.R' (and 'disp')

OrdMonReg_1.0.1 (2009/07/20)

  • Changed description files to emphasis on isotonic (according to revision of paper)

OrdMonReg_1.0.0 (2009/04/10)

  • initial version

Reference manual

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1.0.3 by Kaspar Rufibach, 10 years ago,,

Browse source code at

Authors: Fadoua Balabdaoui , Kaspar Rufibach , Filippo Santambrogio

Documentation:   PDF Manual  

GPL (>= 2) license

See at CRAN