Nonparametic estimation of location and dispersion on Riemannian manifolds

作者: Rabi Bhattacharya , Vic Patrangenaru

DOI: 10.1016/S0378-3758(02)00268-9

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摘要: A central limit theorem for intrinsic means on a complete flat manifold and some asymptotic properties of the total sample variance an arbitrary are given. studentized pivotal statistic its bootstrap analogue which yield confidence regions mean also derived.

参考文章(34)
M. Emery, G. Mokobodzki, Sur le barycentre d'une probabilité dans une variété Séminaire de probabilités de Strasbourg. ,vol. 25, pp. 220- 233 ,(1991) , 10.1007/BFB0100858
John T. Kent, The Complex Bingham Distribution and Shape Analysis Journal of the Royal Statistical Society: Series B (Methodological). ,vol. 56, pp. 285- 299 ,(1994) , 10.1111/J.2517-6161.1994.TB01978.X
C. Radhakrishna Rao, Information and the Accuracy Attainable in the Estimation of Statistical Parameters Bull Calcutta. Math. Soc.. ,vol. 37, pp. 235- 247 ,(1992) , 10.1007/978-1-4612-0919-5_16
Xavier Pennec, Jean-Philippe Thirion, A Framework for Uncertainty and Validation of 3-D RegistrationMethods Based on Points and Frames International Journal of Computer Vision. ,vol. 25, pp. 203- 229 ,(1997) , 10.1023/A:1007976002485
Xavier Pennec, Nicholas Ayache, Uniform Distribution, Distance and Expectation Problems for Geometric Features Processing Journal of Mathematical Imaging and Vision. ,vol. 9, pp. 49- 67 ,(1998) , 10.1023/A:1008270110193
Joseph Albert Wolf, Spaces of Constant Curvature ,(1984)
Colin R. Goodall, Kanti V. Mardia, Projective Shape Analysis Journal of Computational and Graphical Statistics. ,vol. 8, pp. 143- 168 ,(1999) , 10.1080/10618600.1999.10474808
Shyamal Das Peddada, Ted Chang, Bootstrap Confidence Region Estimation of the Motion of Rigid Bodies Journal of the American Statistical Association. ,vol. 91, pp. 231- 241 ,(1996) , 10.1080/01621459.1996.10476681