minK

minK1

minK2

minK3

Internal functions for Dykstra's algorithm to compute bounded monotone regression estimates.

regression

nonparametric

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.

Kaspar Rufibach

OrdMonReg

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

minK function

Compute projections on restriction cones in Dykstra's algorithm.

minK: Compute projections on restriction cones in Dykstra's algorithm.

Description

Arguments

Details

References

See Also