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Title: Confidence region of singular subspaces Authors:  Dong Xia - Hong Kong University of Science and Technology (Hong Kong) [presenting]
Abstract: Spectral methods are prevalent and powerful in low-rank statistical models. Unlike the elegantly established results on the accuracy of point estimates, little is known about statistical inference of low-rank models. We will introduce a simple technical tool for investigating the empirical singular subspaces. Basically, an explicit representation formula is developed for the empirical spectral projector. We then prove the normal approximation of the joint projection distance between the empirical singular subspace and the true singular subspace when the noise matrix has i.i.d. Gaussian entries. We calculate, up to the fourth order, the approximation of the expected joint projection distance. Data-dependent confidence regions are then proposed which achieves any pre-determined confidence level asymptotically.