A1084
Title: Dimension-free rates of bootstrap approximation for spectral statistics in high-dimensional PCA
Authors: Miles Lopes - UC Davis (United States) [presenting]
Abstract: In the context of principal components analysis (PCA), the bootstrap is commonly applied to solve a variety of inference problems, such as constructing confidence intervals for the eigenvalues of the population covariance matrix. However, when the data are high-dimensional, there are relatively few theoretical guarantees that quantify the performance of the bootstrap. A number of recent results will be discussed that establish rates of bootstrap approximation for statistics arising in high-dimensional PCA. Examples include the leading eigenvalues of the sample covariance matrix, as well as the operator norm error of this matrix with respect to the population covariance matrix. Notably, in settings where the population eigenvalues exhibit a decaying structure, the rates of bootstrap approximation are dimension-free.
