Hausdorff moment problem: Reconstruction of probability density functions
AbstractThe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 78 (2008)
Issue (Month): 13 (September)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Gwo Dong Lin, 1997. "On the moment problems," Statistics & Probability Letters, Elsevier, Elsevier, vol. 35(1), pages 85-90, August.
- Chen, Song Xi, 1999. "Beta kernel estimators for density functions," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 31(2), pages 131-145, August.
- Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of distributions," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(12), pages 1612-1618, September.
- Mnatsakanov, Robert M. & Li, Shengqiao, 2013. "The Radon transform inversion using moments," Statistics & Probability Letters, Elsevier, Elsevier, vol. 83(3), pages 936-942.
- Mnatsakanov, Robert M., 2011. "Moment-recovered approximations of multivariate distributions: The Laplace transform inversion," Statistics & Probability Letters, Elsevier, Elsevier, vol. 81(1), pages 1-7, January.
- Mnatsakanov, Robert & Sarkisian, Khachatur, 2012. "Varying kernel density estimation on R+," Statistics & Probability Letters, Elsevier, Elsevier, vol. 82(7), pages 1337-1345.
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