In this paper, we consider the problem of finding the least-squares estimators of two isotonic regression curves [image omitted] and [image omitted] under the additional constraint that they are ordered, for example, ...
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In this paper, we consider the problem of finding the least-squares estimators of two isotonic regression curves [image omitted] and [image omitted] under the additional constraint that they are ordered, for example, [image omitted]. Given two sets of n data points y1, ..., yn and z1, ..., zn observed at (the same) design points, the estimates of the true curves are obtained by minimising the weighted least-squares criterion [image omitted] over the class of pairs of vectors (a, b)nxn such that a1a2 center dot center dot center dot an, b1b2 center dot center dot center dot bn, and aibi, i=1, ..., n. The characterisation of the estimators is established. To compute these estimators, we use an iterative projected subgradient algorithm, where the projection is performed with a 'generalised' pool-adjacent-violaters algorithm, a byproduct of this work. Then, we apply the estimation method to real data from mechanical engineering.
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