Moved definition of mu-bar as requested by referee
Adjusted margins to make editing easier
Separated footnotes 1 and 2 as requested by referee
Making large structural revisions to the paper
minor changes to bootstrap probability measure
Edited main paper
Revising the paper some more

I'm writing up just the CLT approximation on its own first.
Edited proof of Theorem 1 some more
Editing proofs some more
Straightened out part of the clt proof
Made some more revisions to the main result of the paper.
Rewrote main CLT for bootstrap process
Made further edits to theoretical results
Made more changes to proofs.
Made minor changes to proofs of results
Finished typing up reproduction of De Jong's proof
Edited clt proofs some more
Finished very rough version of 2nd moment convergence
Making more revisions
Still working on main proofs