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Convergence Rates for Logspline Tomography

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  • Koo, Ja-Yong

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.

Suggested Citation

  • Koo, Ja-Yong, 1998. "Convergence Rates for Logspline Tomography," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 367-384, November.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:367-384
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    References listed on IDEAS

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    1. Kooperberg, Charles & Stone, Charles J., 1991. "A study of logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 12(3), pages 327-347, November.
    2. Koo, Ja-Yong, 1996. "Bivariate B-splines for tensor logspline density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 21(1), pages 31-42, January.
    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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