Least-squares estimation of two-ordered monotone regression curves

Fadoua Balabdaoui, Kaspar Rufibach and Filippo Santambrogio

Journal of Nonparametric Statistics, 2010, vol. 22, issue 8, 1019-1037

Abstract: 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 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 over the class of pairs of vectors (a, b)∈ℝn×ℝn such that a1≤a2≤···≤an, b1≤b2≤···≤bn, and ai≤bi, 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.

Date: 2010
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DOI: 10.1080/10485250903548729

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