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.

翻译：本文发展了一种渐近方法，用于构建主成分分析中所有线性子空间集合的置信区域，并由此推导出关于该集合的假设检验。我们的方法基于赋予某些线性子空间集合的黎曼流形几何结构。