Supplementary Material for " Bootstrapping the error of Oja's algorithm "

In this document we provide the detailed proofs of results presented in the main manuscript. We also provide the Hoeffding decomposition for the bootstrap in Proposition A.4. In Section B we provide all results needed for a complete proof of Theorem 1. In Sections B.1, B.2, and B.3 we provide the proof of Theorem 1, the adaptation of high dimensional CLT of [8] to our setting and all supporting lemmas, respectively. In Section C we provide all details of the proof of the Bootstrap consistency, i.e.