Add new dummy macros for empirics

The empirics code defines some LaTeX macros that convey design
choices, etc. This commit provides default definitions for them
so that the LaTeX compiles whether or not the simulations have
been run. I've done this before, but must have missed these
macros.
Extensive rewrite of supporting results

- Fix the proofs
- Add results over R+1,...,R'
Add notation and clarification to beginning of appendix

- Defines a few terms that had been accidentally deleted at the beginning
  of the appendix
- Add text specifying that the proofs are for scalars.
Rephrase parts of proof of Theorem 1
Remove redundant theorem from appendix
Tweak wording in introduction to paper
Change Assumption 3 on NED size

The NED size conditions were incorrect; this commit changes them to
the right ones.
Add variance-covariance matrix to Theorem 1
Merge branch 'master' into maths

Conflicts:
	mixedwindow.tex
Merge branch 'master' into maths
Add macros for OOS averages
Add to ignore list
Tweak notation
Add proof of vcv consistency