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arXiv · 1812.04249

Distribution-free properties of isotonic regression

Jake A. Soloff·Adityanand Guntuboyina·Jim Pitman
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Abstract

It is well known that the isotonic least squares estimator is characterized as the derivative of the greatest convex minorant of a random walk. Provided the walk has exchangeable increments, we prove that the slopes of the greatest convex minorant are distributed as order statistics of the running averages. This result implies an exact non-asymptotic formula for the squared error risk of least squares in isotonic regression when the true sequence is constant that holds for every exchangeable error distribution.

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Jake A. Soloff, Adityanand Guntuboyina, Jim Pitman. 2018-12-11. Distribution-free properties of isotonic regression. https://arxiv.org/abs/1812.04249

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