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A stochastic calculus approach to the shape distribution induced by a complex normal model

Published online by Cambridge University Press:  24 October 2008

Huiling Le
Affiliation:
Gonville & Caius College, Cambridge

Abstract

An approach via stochastic calculus was given by Kendall in [7] to the Mardia–Dryden shape distribution of three labelled independent -random points (j = 1, 2, 3). We give here the analogous approach for the general case discussed in [3] in which k labelled random points have a complex normal distribution.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Berger, M., Gauduchon, P. and Mazet, E.. Le Spectre d'une Variété Riemannienne. Lecture Notes in Math. vol. 194 (Springer-Verlag, 1971).Google Scholar
[2]Dieudonné, J.. Foundations of Modern Analysis (Academic Press, 1960).Google Scholar
[3]Dryden, I. L. and Mardia, K. V.. General shape distributions in a plane. Adv. Appl. Probab. (To appear.)Google Scholar
[4]Gallot, S., Hulin, D. and Lafontaine, J.. Riemannian Geometry (Springer-Verlag, 1987).Google Scholar
[5]Helgason, S.. Groups and Geometric Analysis (Academic Press, 1984).Google Scholar
[6]Kendall, D. G.. Shape manifolds, procrustean metrics, and complex projective spaces. Bull London Math. Soc. 16 (1984), 81121.Google Scholar
[7]Kendall, D. G.. The Mardia–Dryden shape distribution for triangles: a stochastic calculus approach. J. Appl. Probab. (To appear.)Google Scholar
[8]Mardia, K. V. and Dryden, I. L.. Shape distributions for landmark data. Adv. Appl. Probab. 21 (1989), 742755.Google Scholar
[9]Rogers, L. C. G. and Williams, D.. Diffusion, Markov Processes, and Martingales: Ito Calculus (John Wiley & Sons, 1987).Google Scholar
[10]Szegö, G.. Orthogonal Polynomials (American Mathematical Society, 1939).Google Scholar
[11]Watson, G. N.. A Treatise on The Theory of Besse1 Functions (Cambridge University Press, 1948).Google Scholar