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Article Dans Une Revue Journal of Nonparametric Statistics Année : 2010

Least Squares estimation of two ordered monotone regression curves

Résumé

In this paper, we consider the problem of finding the least-squares estimators of two isotonic regression curves g ◦ 1 and g ◦ 2 under the additional constraint that they are ordered, for example, g ◦ 1 ≤ g ◦ 2 .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 criterionL2(a, b) = n j=1(yj − aj )2w1,j + n j=1(zj − bj )2w2,j 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.

Dates et versions

hal-00701843 , version 1 (26-05-2012)

Identifiants

Citer

Fadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio. Least Squares estimation of two ordered monotone regression curves. Journal of Nonparametric Statistics, 2010, 22, pp.1019-1037. ⟨10.1080/10485250903548729⟩. ⟨hal-00701843⟩
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