Compute least squares estimates of one bounded or two ordered isotonic regression curves
Compute solution to the problem of two ordered isotonic or antitonic c...
Compute least square estimate of an iso- or antitonic function, bounde...
Compute solution to the problem of two ordered isotonic or antitonic c...
Computes explicitly known values of the estimates in the two ordered f...
Function to display numbers in outputs
Compute least squares criterion for two ordered isotonic regression fu...
Compute bounded weighted average
Compute projections on restriction cones in Dykstra's algorithm.
Compute least squares estimates of one bounded or two ordered antitoni...
Computes a subgradient for the projected subgradient algorithm
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.
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