A geometric framework for asymptotic inference of principal subspaces in PCA

TL;DR

This paper introduces a geometric, Riemannian manifold-based approach for asymptotic inference of principal subspaces in PCA, enabling confidence region construction and hypothesis testing.

Contribution

It presents a novel geometric framework for PCA subspace inference, extending traditional methods with Riemannian geometry techniques.

Findings

Provides asymptotic confidence regions for PCA subspaces

Enables hypothesis testing on principal subspaces

Utilizes Riemannian geometry for statistical inference

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.