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.
Package details 


Author  Fadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio 
Maintainer  Kaspar Rufibach <[email protected]> 
License  GPL (>= 2) 
Version  1.0.3 
URL  http://www.ceremade.dauphine.fr/~fadoua http://www.kasparrufibach.ch http://www.math.upsud.fr/~santambr/ 
Package repository  View on CRAN 
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