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On the truncated Hausdorff moment problem under Sobolev regularity conditions

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  • Zellinger, Werner
  • Moser, Bernhard A.

Abstract

We study the problem of approximating the recovery of a probability distribution on the unit interval from its first k moments. As main result we obtain an upper bound on the L1 reconstruction error under the regularity assumption that the log-density function has square-integrable derivatives up to some natural order r>1. Our bound is of order O(k−r). A comparative study relates our findings to alternative conditions on the distributions.

Suggested Citation

  • Zellinger, Werner & Moser, Bernhard A., 2021. "On the truncated Hausdorff moment problem under Sobolev regularity conditions," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321001053
    DOI: 10.1016/j.amc.2021.126057
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    References listed on IDEAS

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    1. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    2. Tardella, Luca, 2001. "A note on estimating the diameter of a truncated moment class," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 115-124, September.
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    Cited by:

    1. Baishuai Zuo & Chuancun Yin, 2022. "Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures," Papers 2203.00839, arXiv.org.

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