I have really enjoyed the pdf document with ugly(!) math. Thanks so much for such a clear and readable exposition.
I am thinking that equations (11) and (12) are missing the outcome variables y_i(z_i) so that the mean of their difference can be associated with ATE. Am I correct?
I think "-2^{-m0}" appearing in both of them are "+2^{-m0}". I am not very certain though.
Also, I think the proof of Theorem 1.1 is also given for z_* = 1, which also implies \Delta = ATE > 0 . This helped me to understand inequalities for the difference of \hat{\mu}'s. Again not very much sure about this. If this is the case, it may worth repeating for folks like me...
What's the problem with gambling terms?
I have really enjoyed the pdf document with ugly(!) math. Thanks so much for such a clear and readable exposition.
I am thinking that equations (11) and (12) are missing the outcome variables y_i(z_i) so that the mean of their difference can be associated with ATE. Am I correct?
Yes, you are correct. Thanks. I fixed it and reposted the pdf.
Could you please check equations (33) and (34)?
I think "-2^{-m0}" appearing in both of them are "+2^{-m0}". I am not very certain though.
Also, I think the proof of Theorem 1.1 is also given for z_* = 1, which also implies \Delta = ATE > 0 . This helped me to understand inequalities for the difference of \hat{\mu}'s. Again not very much sure about this. If this is the case, it may worth repeating for folks like me...
(I will delete these comments later.)