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Stieltjes and Hamburger Reduced Moment Problem When MaxEnt Solution Does Not Exist

Author

Listed:
  • Pier Luigi Novi Inverardi

    (Department of Economics and Management, University of Trento, 38122 Trento, Italy)

  • Aldo Tagliani

    (Department of Economics and Management, University of Trento, 38122 Trento, Italy)

Abstract

For a given set of moments whose predetermined values represent the available information, we consider the case where the Maximum Entropy (MaxEnt) solutions for Stieltjes and Hamburger reduced moment problems do not exist. Genuinely relying upon MaxEnt rationale we find the distribution with largest entropy and we prove that this distribution gives the best approximation of the true but unknown underlying distribution. Despite the nice properties just listed, the suggested approximation suffers from some numerical drawbacks and we will discuss this aspect in detail in the paper.

Suggested Citation

  • Pier Luigi Novi Inverardi & Aldo Tagliani, 2021. "Stieltjes and Hamburger Reduced Moment Problem When MaxEnt Solution Does Not Exist," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:309-:d:493208
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    References listed on IDEAS

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    1. Milev, Mariyan & Tagliani, Aldo, 2017. "Entropy convergence of finite moment approximations in Hamburger and Stieltjes problems," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 114-117.
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    Cited by:

    1. Octav Olteanu, 2022. "Markov Moment Problem and Sandwich Conditions on Bounded Linear Operators in Terms of Quadratic Forms," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    2. Octav Olteanu, 2022. "Convexity, Markov Operators, Approximation, and Related Optimization," Mathematics, MDPI, vol. 10(15), pages 1-17, August.

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