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Least Squares estimation of two ordered ...
Balabdaoui, Fadoua...

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Least Squares estimation of two ordered monotone regression curves by Balabdaoui, Fadoua ( Author )
Lemonjar Open Access
N.A
14-04-2009
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; e.g., 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 minimizing the weighted Least Squares criterion L2(a,b)=∑nj=1(yj−aj)2w1,j+∑nj=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 characterization of the estimators is established. To compute these estimators, we use an iterative projected subgradient algorithm, where the projection is performed with a "generalized" pool-adjacent-violaters algorithm (PAVA), a byproduct of this work. Then, we apply the estimation method to real data from mechanical engineering.
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MYR 0.00
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https://arxiv.org/abs/0904.2052
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