Consistent Estimation of a Class of Distances Between Covariance Matrices
This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. This family of dis...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) |
| Repositorio: | r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) |
| OAI Identifier: | oai:cttc.fundanetsuite.com:p8502 |
| Acceso en línea: | https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=8502 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85204783191&doi=10.1109%2fTIT.2024.3464678&partnerID=40&md5=1971e5f07ee3e02c2aac3f087799a4f1 |
| Access Level: | acceso abierto |
| Palabra clave: | Factor analysis Multivariant analysis Central Limit Theorem Consistent estimation Covariance matrices Covariance matrix distance Euclidean distance Matrix distances Random matrices theory Riemannian geometry Riemannian manifold Traces of functions Matrix algebra |
| Sumario: | This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are separately applied to each covariance matrix. This family of distances is particularly useful as it takes into consideration the fact that covariance matrices lie in the Riemannian manifold of positive definite matrices, thereby including a variety of commonly used metrics, such as the Euclidean distance, Jeffreys' divergence, and the log-Euclidean distance. Moreover, a statistical analysis of the asymptotic behavior of this class of distance estimators has also been conducted. Specifically, we present a central limit theorem that establishes the asymptotic Gaussianity of these estimators and provides closed form expressions for the corresponding means and variances. Empirical evaluations demonstrate the superiority of our proposed consistent estimator over conventional plug-in estimators in multivariate analytical contexts. Additionally, the central limit theorem derived in this study provides a robust statistical framework to assess of accuracy of these estimators. © 2024 IEEE. |
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