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Least-squares estimation of two-ordered monotone regression curves

Author

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  • Fadoua Balabdaoui
  • Kaspar Rufibach
  • Filippo Santambrogio

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.

Suggested Citation

  • Fadoua Balabdaoui & Kaspar Rufibach & Filippo Santambrogio, 2010. "Least-squares estimation of two-ordered monotone regression curves," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 1019-1037.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:8:p:1019-1037
    DOI: 10.1080/10485250903548729
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