The Annals of Statistics

Multivariate Aspects of Shape Theory

Colin R. Goodall and Kanti V. Mardia

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Abstract

We place shape theory in the setting of noncentral multivariate analysis, and thus provide a comprehensive view of shape distributions when landmark coordinates are Gaussian distributed. This work allows the statistical analysis of shape to be carried out using standard techniques of multivariate analysis. The paper includes some new results in all dimensions and a general Gaussian approximation to the size-and-shape distribution. We also discuss some inference problems and give a numerical example.

Article information

Source
Ann. Statist., Volume 21, Number 2 (1993), 848-866.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349154

Digital Object Identifier
doi:10.1214/aos/1176349154

Mathematical Reviews number (MathSciNet)
MR1232522

Zentralblatt MATH identifier
0788.62045

JSTOR
links.jstor.org

Subjects
Primary: 62H10: Distribution of statistics
Secondary: 62H11: Directional data; spatial statistics 62E15: Exact distribution theory 62E17: Approximations to distributions (nonasymptotic)

Keywords
Shape size-and-shape zonal polynomial Gaussian model configuration singular values distribution theory polar coordinates small variations QR decomposition

Citation

Goodall, Colin R.; Mardia, Kanti V. Multivariate Aspects of Shape Theory. Ann. Statist. 21 (1993), no. 2, 848--866. doi:10.1214/aos/1176349154. https://projecteuclid.org/euclid.aos/1176349154


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