Bootstrapping the error of Oja's algorithm. (arXiv:2106.14857v2 [math.ST] UPDATED)

We consider the problem of quantifying uncertainty for the estimation error
of the leading eigenvector from Oja's algorithm for streaming principal
component analysis, where the data are generated IID from some unknown
distribution. By combining classical tools from the U-statistics literature
with recent results on high-dimensional central limit theorems for quadratic
forms of random vectors and concentration of matrix products, we establish a
weighted $\chi^2$ approximation result for the $\sin^2$ error between the
population eigenvector and the output of Oja's …

algorithm arxiv bootstrapping error math