Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Evaluation of the Efficiency of an Inverse Exponential Kernel Estimator for Spherical Data

  • Park, Hyun Suk (Department of Finance and Information Statistics, Hallym University)
  • Received : 2012.08.03
  • Accepted : 2013.01.10
  • Published : 2013.01.31
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Abstract

This paper deals with the relative efficiency of two kernel estimators $\hat{f}_n$ and $\hat{g}_n$ by using spherical data, as proposed by Park (2012), and Bai et al. (1988), respectively. For this, we suggest the computing flows for the relative efficiency on the 2-dimensional unit sphere. An evaluation procedure between two estimators (given the same kernels) is also illustrated through the observed data on normals to the orbital planes of long-period comets.

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References

  1. Bai, Z. D., Rao, C. R. and Zaho, L. C. (1988). Kernel estimators of density function of directional data, Journal of Multivariate Analysis, 27, 24-39. https://doi.org/10.1016/0047-259X(88)90113-3
  2. Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis, Clarendon press, Oxford.
  3. Dhillon, I. S. and Sra, S. (2003). Modeling data using directional distributions, Technical Report No. TR-03-06, The University of Texas at Austin.
  4. Fisher, N. I., Lewis, T. and Embleton, B. J. (1993). Statistical Analysis of Spherical Data, Cambridge, Cambridge University Press, England.
  5. Fletcher, P., Lu, C. and Joshi, S. (2003). Statistics of shape via principal geodesic analysis on lie groups, In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Madison, WI, 1, 95-101.
  6. Hall, P.,Watson, G. and Cabrera, J. (1987). Kernel density estimation with spherical data, Biometrika, 74, 751-762. https://doi.org/10.1093/biomet/74.4.751
  7. Kim, Y. T. and Park, H. S. (2012). Geometric structures arising from kernel density estimation on Riemannian manifolds, Journal of Multivariate Analysis, 114, 112-126.
  8. Park, H. S. (2012). Asymptotic behavior of the kernel density estimator from a geometric viewpoint, Communications in Statistics - Theory and Methods, 41, 3479-3496. https://doi.org/10.1080/03610926.2011.585009
  9. Watson, G. S. (1983). Statistics on Spheres, Wiley, New York.