IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i13p1869-1877.html
   My bibliography  Save this article

Hausdorff moment problem: Reconstruction of probability density functions

Author

Listed:
  • Mnatsakanov, Robert M.

Abstract

The problem of recovering a moment-determinate probability density function (pdf) from its moments is studied. The proposed construction provides a method for recovery of different pdfs via simple transformations of the moment sequences. Uniform and L1-rates of convergence of moment-recovered pdfs are obtained. Finally, some applications and examples are briefly discussed.

Suggested Citation

  • Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1869-1877
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00053-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 85-90, August.
    2. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    3. Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 131-145, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Robert M. Mnatsakanov & Hansjoerg Albrecher & Stephane Loisel, 2022. "Approximations of Copulas via Transformed Moments," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3175-3193, December.
    2. Hansjörg Albrecher & José Carlos Araujo-Acuna, 2022. "On The Randomized Schmitter Problem," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 515-535, June.
    3. Mnatsakanov, Robert M., 2011. "Moment-recovered approximations of multivariate distributions: The Laplace transform inversion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 1-7, January.
    4. Calès, Ludovic & Chalkis, Apostolos & Emiris, Ioannis Z., 2019. "On the cross-sectional distribution of portfolio returns," JRC Working Papers in Economics and Finance 2019-11, Joint Research Centre, European Commission.
    5. Ludovic Cal`es & Apostolos Chalkis & Ioannis Z. Emiris, 2021. "The cross-sectional distribution of portfolio returns and applications," Papers 2105.06573, arXiv.org.
    6. Gzyl, Henryk & Novi Inverardi, Pierluigi & Tagliani, Aldo, 2015. "Entropy and density approximation from Laplace transforms," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 225-236.
    7. Mnatsakanov, Robert M. & Pommeret, Denys, 2024. "On recovering the relative distribution, Part 1: The moment-recovered approach," Statistics & Probability Letters, Elsevier, vol. 208(C).
    8. Mnatsakanov, Robert M. & Li, Shengqiao, 2013. "The Radon transform inversion using moments," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 936-942.
    9. Mnatsakanov, Robert M. & Sarkisian, Khachatur & Hakobyan, Artak, 2015. "Approximation of the ruin probability using the scaled Laplace transform inversion," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 717-727.
    10. Diel, Roland & Lerasle, Matthieu, 2018. "Non parametric estimation for random walks in random environment," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 132-155.
    11. Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1337-1345.
    12. Weimei Li & Leifu Gao, 2024. "Research on Risk-Averse Procurement Optimization of Emergency Supplies for Mine Thermodynamic Disasters," Mathematics, MDPI, vol. 12(14), pages 1-17, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1612-1618, September.
    2. Hirukawa, Masayuki, 2010. "Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 473-495, February.
    3. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    4. Hagmann, M. & Scaillet, O., 2007. "Local multiplicative bias correction for asymmetric kernel density estimators," Journal of Econometrics, Elsevier, vol. 141(1), pages 213-249, November.
    5. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    6. Salvatore D. Tomarchio & Antonio Punzo, 2019. "Modelling the loss given default distribution via a family of zero‐and‐one inflated mixture models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(4), pages 1247-1266, October.
    7. Grammig, Joachim G. & Peter, Franziska J., 2008. "International price discovery in the presence of market microstructure effects," CFR Working Papers 08-10, University of Cologne, Centre for Financial Research (CFR).
    8. Song Li & Mervyn J. Silvapulle & Param Silvapulle & Xibin Zhang, 2015. "Bayesian Approaches to Nonparametric Estimation of Densities on the Unit Interval," Econometric Reviews, Taylor & Francis Journals, vol. 34(3), pages 394-412, March.
    9. Christophe Gaillac & Eric Gautier, 2021. "Nonparametric classes for identification in random coefficients models when regressors have limited variation," Working Papers hal-03231392, HAL.
    10. Ostrovska, Sofiya & Stoyanov, Jordan, 2010. "A new proof that the product of three or more exponential random variables is moment-indeterminate," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 792-796, May.
    11. J. Baixauli & Susana Alvarez, 2012. "Implied Severity Density Estimation: An Extended Semiparametric Method to Compute Credit Value at Risk," Computational Economics, Springer;Society for Computational Economics, vol. 40(2), pages 115-129, August.
    12. Gzyl, Henryk & Novi-Inverardi, Pier-Luigi & Tagliani, Aldo, 2013. "Determination of the probability of ultimate ruin by maximum entropy applied to fractional moments," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 457-463.
    13. Faugeras, Olivier P., 2009. "A quantile-copula approach to conditional density estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2083-2099, October.
    14. Nagler Thomas & Schellhase Christian & Czado Claudia, 2017. "Nonparametric estimation of simplified vine copula models: comparison of methods," Dependence Modeling, De Gruyter, vol. 5(1), pages 99-120, January.
    15. Gery Geenens, 2014. "Probit Transformation for Kernel Density Estimation on the Unit Interval," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 346-358, March.
    16. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K., 2007. "Nonparametric density estimation for multivariate bounded data," LIDAM Discussion Papers CORE 2007065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
    18. Yasmina Ziane & Nabil Zougab & Smail Adjabi, 2018. "Birnbaum–Saunders power-exponential kernel density estimation and Bayes local bandwidth selection for nonnegative heavy tailed data," Computational Statistics, Springer, vol. 33(1), pages 299-318, March.
    19. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    20. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1869-1877. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.