Least-squares estimation of two-ordered monotone regression curves

作者：Balabdaoui Fadoua; Rufibach Kaspar^*; Santambrogio Filippo

来源：Journal of Nonparametric Statistics, 2010, 22(8): 1019-1037.

DOI：10.1080/10485250903548729

• least squares
• monotone regression
• pool-adjacent-violaters algorithm
• shape constraint estimation
• subgradient algorithm

In this paper, we consider the problem of finding the least-squares estimators of two isotonic regression curves [image omitted] and [image omitted] under the additional constraint that they are ordered, for example, [image omitted]. 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 [image omitted] over the class of pairs of vectors (a, b)nxn such that a1a2 center dot center dot center dot an, b1b2 center dot center dot center dot bn, and aibi, 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.

• 出版日期2010