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Uncoupled Isotonic Regression with Discrete Errors

In: Advances in Contemporary Statistics and Econometrics

Author

Listed:
  • Jan Meis

    (Heidelberg University, Institute of Medical Biometry and Informatics)

  • Enno Mammen

    (Heidelberg University, Institute of Applied Mathematics)

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.

Suggested Citation

  • Jan Meis & Enno Mammen, 2021. "Uncoupled Isotonic Regression with Discrete Errors," Springer Books, in: Abdelaati Daouia & Anne Ruiz-Gazen (ed.), Advances in Contemporary Statistics and Econometrics, pages 123-135, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-73249-3_7
    DOI: 10.1007/978-3-030-73249-3_7
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