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

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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.

Author
Fadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio
Date of publication
2011-12-01 08:00:09
Maintainer
Kaspar Rufibach <kaspar.rufibach@gmail.com>
License
GPL (>= 2)
Version
1.0.3
URLs

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Man pages

BoundedAntiMeanTwo
Compute solution to the problem of two ordered isotonic or...
BoundedIsoMean
Compute least square estimate of an iso- or antitonic...
BoundedIsoMeanTwoDykstra
Compute solution to the problem of two ordered isotonic or...
bstar_n
Computes explicitly known values of the estimates in the two...
disp
Function to display numbers in outputs
LSfunctional
Compute least squares criterion for two ordered isotonic...
MA
Compute bounded weighted average
mechIng
Mechanical engineering dataset used to illustrate ordered...
minK
Compute projections on restriction cones in Dykstra's...
ordMonReg-package
Compute least squares estimates of one bounded or two ordered...
Subgradient
Computes a subgradient for the projected subgradient...

Files in this package

OrdMonReg
OrdMonReg/MD5
OrdMonReg/R
OrdMonReg/R/Subgradient.r
OrdMonReg/R/minK3.r
OrdMonReg/R/minK2.r
OrdMonReg/R/minK1.r
OrdMonReg/R/MA.r
OrdMonReg/R/LSfunctional.r
OrdMonReg/R/disp.r
OrdMonReg/R/bstar_n.r
OrdMonReg/R/BoundedIsoMeanTwoDykstra.r
OrdMonReg/R/BoundedIsoMeanTwo.r
OrdMonReg/R/BoundedIsoMean.r
OrdMonReg/R/BoundedAntiMeanTwo.r
OrdMonReg/R/BoundedAntiMean.r
OrdMonReg/R/astar_1.r
OrdMonReg/NEWS
OrdMonReg/NAMESPACE
OrdMonReg/man
OrdMonReg/man/Subgradient.Rd
OrdMonReg/man/ordMonReg-package.Rd
OrdMonReg/man/minK.Rd
OrdMonReg/man/mechIng.Rd
OrdMonReg/man/MA.Rd
OrdMonReg/man/LSfunctional.Rd
OrdMonReg/man/disp.Rd
OrdMonReg/man/bstar_n.Rd
OrdMonReg/man/BoundedIsoMeanTwoDykstra.Rd
OrdMonReg/man/BoundedIsoMean.Rd
OrdMonReg/man/BoundedAntiMeanTwo.Rd
OrdMonReg/DESCRIPTION
OrdMonReg/data
OrdMonReg/data/mechIng.rda