ordMonReg-package: Compute least squares estimates of one bounded or two ordered...

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

Description

We consider the problem of estimating two isotonic regression curves g^\circ_1 and g^\circ_2 under the constraint that g^\circ_1 ≤ g^\circ_2. 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) = ∑_{i=1}^n (y_i - a_i)^2 w_1(x_i) + ∑_{i=1}^n (z_i - b_i)^2 w_2(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 pool-adjacent-violaters algorithm (PAVA) as well as Dykstra's cyclical projection algorithm..

Additionally, functions to solve the bounded isotonic regression problem described in Barlow et al. (1972, p. 57) are provided.

Details

Package:	OrdMonReg
Type:	Package
Version:	1.0.3
Date:	2011-11-30
License:	GPL (>=2)

Author(s)

Fadoua Balabdaoui [e-mail]
http://www.ceremade.dauphine.fr/~fadoua

Kaspar Rufibach (maintainer) [e-mail]
http://www.kasparrufibach.ch

Filippo Santambrogio [e-mail]
http://www.math.u-psud.fr/~santambr/

References

Balabdaoui, F., Rufibach, K., Santambrogio, F. (2009). Least squares estimation of two ordered monotone regression curves. Preprint.

Barlow, R. E., Bartholomew, D. J., Bremner, J. M., Brunk, H. D. (1972). Statistical inference under order restrictions. The theory and application of isotonic regression. John Wiley and Sons, London - New York - Sydney.

Dykstra, R.L. (1983). An Algorithm for Restricted Least Squares Regression. J. Amer. Statist. Assoc., 78, 837–842.

See Also

Other versions of bounded regression are implemented in the packages cir, Iso, monreg. The function BoundedIsoMean is a generalization of the function isoMean in the package logcondens.

Examples

## examples are provided in the help files of the main functions of this package:
?BoundedAntiMean
?BoundedAntiMeanTwo

OrdMonReg documentation built on May 2, 2019, 1:45 p.m.