A geometric framework for asymptotic inference of principal subspaces in PCA
arXiv:2209.02025
Abstract
In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on this set. Our method is based on the geometry of Riemannian manifolds with which some sets of linear subspaces are endowed.
References in corpus (5)
- Large sample theory of intrinsic and extrinsic sample means on manifolds--II
- A Grassmann Manifold Handbook: Basic Geometry and Computational Aspects
- Maximum Entropy on Compact Groups
- The curse of isotropy: from principal components to principal subspaces
- Effective formulas for the geometry of normal homogeneous spaces. Application to flag manifolds