Abstract (EN)

In this paper, we consider the problem of finding the least-squares estimators of two isotonic regression curves and under the additional constraint that they are ordered, for example, . Given two sets of n data points y 1, …, y n and z 1, …, z n observed at (the same) design points, the estimates of the true curves are obtained by minimising the weighted least-squares criterion over the class of pairs of vectors (a, b) n × n such that a 1≤a 2≤···≤a n , b 1≤b 2≤···≤b n , and a i ≤b i , 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.