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Convergence Rates for Logspline Tomography

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  • Koo, Ja-Yong
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    Abstract

    We consider bivariate logspline density estimation for tomography data. In the usual logspline density estimation for bivariate data, the logarithm of the unknown density function is estimated by tensor product splines, the unknown parameters of which are given by maximum likelihood. In this paper we use tensor product B-splines and the projection-slice theorem to construct the logspline density estimators for tomography data. Rates of convergence are established for log-density functions assumed to belong to a Besov space.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 67 (1998)
    Issue (Month): 2 (November)
    Pages: 367-384

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    Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:367-384

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    Related research

    Keywords: logspline models; tensor product B-splines; positron emission tomography; projection-slice theorem; Besov space; rate of convergence;

    References

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    1. Koo, Ja-Yong, 1996. "Bivariate B-splines for tensor logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 31-42, January.
    2. Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
    3. Koo, Ja-Yong & Kim, Woo-Chul, 1996. "Wavelet density estimation by approximation of log-densities," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 271-278, February.
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