Electronic Journal of Statistics

Estimation of mean form and mean form difference under elliptical laws

José A. Díaz-García and Francisco J. Caro-Lopera

Full-text: Open access

Abstract

The matrix variate elliptical generalization of [30] is presented in this work. The published Gaussian case is revised and modified. Then, new aspects of identifiability and consistent estimation of mean form and mean form difference are considered under elliptical laws. For example, instead of using the Euclidean distance matrix for the consistent estimates, exact formulae are derived for the moments of the matrix $\mathbf{B}=\mathbf{X}^{c}\left(\mathbf{X}^{c}\right)^{T}$; where $\mathbf{X}^{c}$ is the centered landmark matrix. Finally, a complete application in Biology is provided; it includes estimation, model selection and hypothesis testing.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 2424-2460.

Dates
Received: August 2015
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1496131237

Digital Object Identifier
doi:10.1214/17-EJS1289

Mathematical Reviews number (MathSciNet)
MR3656497

Zentralblatt MATH identifier
1365.62198

Subjects
Primary: 62E15: Exact distribution theory 62E05 62H12: Estimation
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20] 62H35: Image analysis

Keywords
Coordinate free approach non-central singular Pseudo-Wishart distribution matrix variate elliptical distribution matrix variate Gaussian distribution statistical shape theory

Rights
Creative Commons Attribution 4.0 International License.

Citation

Díaz-García, José A.; Caro-Lopera, Francisco J. Estimation of mean form and mean form difference under elliptical laws. Electron. J. Statist. 11 (2017), no. 1, 2424--2460. doi:10.1214/17-EJS1289. https://projecteuclid.org/euclid.ejs/1496131237


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