OrdMonReg-package {OrdMonReg}R Documentation

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

Description

We consider the problem of estimating two antitonic regression curves g_1^* and g_2^* under the constraint that g_1^* >= g_2^*. Given two sets of n data points g_1(x_1), ..., g_1(x_n) and g_2(x_1), ..., g_2(x_n) that are observed at (the same) deterministic points x_1, ..., x_n, the estimates are obtained by minimizing the Least Squares criterion

L(f_1, f_2) = sum_{i=1}^n (g_1(x_i) - f_1(x_i))^2 w_1(x_i)+ sum_{i=1}^n (g_2(x_i) - f_2(x_i))^2 w_2(x_i)

over the class of pairs of functions (f_1, f_2) such that f_1 and f_2 are antitonic and f_1(x_i) >= f_2(x_i) for all i = {1, ..., n}. The estimates are computed with an projected subgradient algorithm where the projection is calculated using a suitable version of the pool-adjacent-violaters algorithm (PAVA).

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

Details

Package: OrdMonReg
Type: Package
Version: 1.0.0
Date: 2009-04-10
License: GPL (>=2)

Author(s)

Fadoua Balabdaoui fadoua@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~fadoua

Kaspar Rufibach (maintainer) kaspar.rufibach@ifspm.uzh.ch
http://www.biostat.uzh.ch/aboutus/people/rufibach.html

Filippo Santambrogio filippo@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~filippo

References

Balabdaoui, F., Rufibach, K., Santambrogio, F. (2009). Least squares estimation of two ordered antitonic 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.

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

[Package OrdMonReg version 1.0.0 Index]