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OrdMonReg (version 1.0.3)

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

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.

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Install

install.packages('OrdMonReg')

Monthly Downloads

167

Version

1.0.3

License

GPL (>= 2)

Maintainer

Last Published

December 1st, 2011

Functions in OrdMonReg (1.0.3)

astar_1, bstar_n

Computes explicitly known values of the estimates in the two ordered functions antitonic regression problem
OrdMonReg-package

Compute least squares estimates of one bounded or two ordered antitonic regression curves
MA

Compute bounded weighted average
mechIng

Mechanical engineering dataset used to illustrate ordered isotonic regression
BoundedIsoMeanTwoDykstra

Compute solution to the problem of two ordered isotonic or antitonic curves
disp

Function to display numbers in outputs
minK

Compute projections on restriction cones in Dykstra's algorithm.
BoundedAntiMean, BoundedIsoMean

Compute least square estimate of an iso- or antitonic function, bounded below and above by fixed functions
BoundedAntiMeanTwo, BoundedIsoMeanTwo

Compute solution to the problem of two ordered isotonic or antitonic curves
Subgradient

Computes a subgradient for the projected subgradient algorithm
LSfunctional

Compute least squares criterion for two ordered isotonic regression functions