Date
2010
Lien vers un document non conservé dans cette base
http://arxiv.org/abs/0904.2052
Indexation documentaire
Probabilités et mathématiques appliquées
Subject
subgradient algorithm; shape constraint estimation; pool-adjacent-violaters algorithm; monotone regression; least squares
Nom de la revue
Journal of Nonparametric Statistics
Volume
22
Numéro
8
Date de publication
2010
Pages article
1019-1037
Nom de l'éditeur
American Statistical Association
Auteur
Santambrogio, Filippo
Rufibach, Kaspar
Balabdaoui, Fadoua
Type
Article accepté pour publication ou publié
Résumé en anglais
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.