| 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 isotonic regression curves g^\circ_1 and g^\circ_2 under the
constraint that g^\circ_1 \le g^\circ_2. Given two sets of n data points y_1, \ldots, y_n
and z_1, \ldots, z_n
that are observed at (the same) deterministic design points x_1, \ldots, x_n, the estimates are obtained by
minimizing the Least Squares criterion
L(a, b) = \sum_{i=1}^n (y_i - a_i)^2 w_1(x_i) + \sum_{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 \le b_i for all i = {1, \ldots, 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 fadoua@ceremade.dauphine.fr
http://www.ceremade.dauphine.fr/~fadoua
Kaspar Rufibach (maintainer) kaspar.rufibach@gmail.com
http://www.kasparrufibach.ch
Filippo Santambrogio filippo.santambrogio@math.u-psud.fr
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