OrdMonReg-package {OrdMonReg} | R Documentation |
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.
Package: | OrdMonReg |
Type: | Package |
Version: | 1.0.0 |
Date: | 2009-04-10 |
License: | GPL (>=2) |
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
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.
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 are provided in the help files of the main functions of this package: ?BoundedAntiMean ?BoundedAntiMeanTwo