Grassmannian Estimation
Claude Auderset, Christian Mazza, Ernst Ruh
TL;DR
This paper investigates the statistical properties of distributions on Grassmannians, providing conditions for the existence and uniqueness of maximum likelihood estimates of the covariance matrix.
Contribution
It introduces a new criterion for the existence and uniqueness of maximum likelihood estimates on Grassmannian distributions.
Findings
Established an existence criterion for MLE on Grassmannians.
Proved uniqueness conditions for the covariance matrix estimate.
Enhanced understanding of statistical inference on Grassmannian manifolds.
Abstract
This paper discusses the family of distributions on the Grassmannian of the linear span of r central gaussian vectors parametrized by the covariance matrix. Our main result is an existence and uniqueness criterion for the maximum likelihood estimate of a sample.
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Taxonomy
TopicsAdvanced Statistical Methods and Models · Point processes and geometric inequalities · Mathematical Inequalities and Applications