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Density Deconvolution in the Circular Structural Model

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  • Goldenshluger, Alexander

Abstract

We consider deconvolving bivariate irregular densities supported on the circumference of the unit circle. The errors are bivariate, and the observations are available on the plane. Assuming that the estimated density is smooth on the circle, we compute exact asymptotics of the minimax risks and develop asymptotically optimal estimators for the case of normal errors. The proposed estimators are automatically sharp minimax adaptive over a wide collection of smoothness classes. It is shown that the same rates of convergence hold for a variety of different types of error distributions. The interesting feature of the problem is that the optimal rates of convergence do not depend on the error distribution and are determined essentially by the problem geometry.

Suggested Citation

  • Goldenshluger, Alexander, 2002. "Density Deconvolution in the Circular Structural Model," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 360-375, May.
    • Handle: RePEc:eee:jmvana:v:81:y:2002:i:2:p:360-375
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    References listed on IDEAS

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    1. Healy, Dennis M. & Hendriks, Harrie & Kim, Peter T., 1998. "Spherical Deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 1-22, October.
    2. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
    3. Hardle, Wolfgang & Tsybakov, A. B., 1993. "How sensitive are average derivatives?," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 31-48, July.
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    Cited by:

    1. Kim, Peter T. & Koo, Ja-Yong & Park, Heon Jin, 2004. "Sharp minimaxity and spherical deconvolution for super-smooth error distributions," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 384-392, August.
    2. Koo, Ja-Yong & Kim, Peter T., 2008. "Sharp adaptation for spherical inverse problems with applications to medical imaging," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 165-190, February.
    3. Kim, Peter T. & Koo, Ja-Yong & Luo, Zhi-Ming, 2009. "Weyl eigenvalue asymptotics and sharp adaptation on vector bundles," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1962-1978, October.

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