Uncoupled Isotonic Regression with Discrete Errors

Jan Meis () and Enno Mammen ()
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Jan Meis: Heidelberg University, Institute of Medical Biometry and Informatics
Enno Mammen: Heidelberg University, Institute of Applied Mathematics

A chapter in Advances in Contemporary Statistics and Econometrics, 2021, pp 123-135 from Springer

Abstract: Abstract In Rigollet and Weed (2019), an estimator was proposed for the uncoupled isotonic regression problem. It was shown that a so-called minimum Wasserstein deconvolution estimator achieves the rate $$\log \log n / \log n$$ log log n / log n . Furthermore, it was shown that for normally distributed errors, this rate is optimal. In this note, we will show that for error distributions supported on a finite set of points, this rate can be improved to the order of $$n ^{-1/(2p)}$$ n - 1 / ( 2 p ) for L $$_p$$ p -risks. We also show that this rate is optimal and cannot be improved for Bernoulli errors.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-73249-3_7

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DOI: 10.1007/978-3-030-73249-3_7

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