Consistency of procrustes estimators

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 59, Issue 1, 1997, Pages 281-290

  Kent, John T ^a   Mardia, Kanti V ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Decentred uniform distribution; Form; Isotropy; Offset uniform distribution; Shape

Indexed keywords

EID: 0001012387     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00069     Document Type: Article

References (17)

1. Bookstein, F. L. (1986) Size and shape spaces for landmark data in two dimensions (with discussion). Statist. Sci., 1, 181-242.
2. _ (1991) Morphometric Tools for Landmark Data: Geometry and Biology. Cambridge: Cambridge University Press.
3. Boulerice, B. and Ducharme, G. R. (1994) Decentered directional data. Ann. Inst. Statist. Math., 46, 573-586.
4. Dryden, I. L. and Mardia, K. V. (1991) General shape distributions in a plane. Adv. Appl. Probab., 23, 259-276.
5. Goodall, C. (1991) Procrustes methods in the statistical analysis of shape (with discussion). J. R. Statist. Soc. B, 53, 285-339.
6. _ (1993) Linear-spectral estimation of means in the presence of nuisance parameters. Technical Report 93-08. Department of Statistics, Pennsylvania State University, State College.
7. Goodall, C. R. and Mardia, K. V. (1993) Multivariate aspects of shape theory. Ann. Statist., 21, 848-866.
8. Gradshteyn, I. S. and Ryzhik, I. M. (1980) Table of Integrals, Series and Products. Orlando: Academic Press.
9. Kendall, D. G. (1984) Shape-manifolds, procrustean metrics and complex projective spaces. Bull. Lond. Math. Soc., 16, 81-121.
10. Kent, J. T. (1992) New directions in shape analysis. In The Art of Statistical Science (ed. K. V. Mardia), pp. 115-127. Chichester: Wiley.
11. _ (1994) The complex Bingham distribution and shape analysis. J. R. Statist. Soc. B, 56, 285-299.
12. Lele, S. (1993) Euclidean distance matrix analysis (EDMA): estimation of mean form and mean form difference. Math. Geol, 25, 573-602.
13. Mardia, K. V. (1972) The Statistics of Directional Data. London: Academic Press.
14. Mardia, K. V. and Dryden, I. L. (1989a) Statistical analysis of shape data. Biometrika, 76, 271-281.
15. _ (1989b) Shape distributions for landmark data. Adv. Appl. Probab., 21, 742-755.
16. _ (1994) Shape averages and their bias. Adv. Appl. Probab., 26, 334-340.
17. Stoyan, D. (1990) Estimation of distances and variances in Bookstein's landmark model. Biometr. J., 32, 843-849.