@whuber After your comments (thank you), I modified this post, but kept it deleted since you had placed the OP on hold, and you were kind enough to share your thoughts about it. I have very little appetite for reopening the answer, but I would like to know if it is now a bit more clear, and if not, whether you could let me know the concept that I am missing. For instance, I am not clear on Jeremias K comment about the kind of dependence allowed.

@Glen_b Glen, I hope that reproducing Sheldon Ross' derivation on CV is acceptable. I have made the source clear. Here

I am not a lawyer, and there's no sense in which I represent StackExchange so you can't take this as in any sense saying it's okay, but in my completely lay understanding, reproducing the form of a derivation with credit should be fine (and if it's not, we're all in trouble). If you're reproducing mathematics verbatim including text explanations it might be reasonable to do quite short passages, as long as the quoted parts are clearly indicated as

such (not all these points relate to copyright; there's an element of what's seen as academically acceptable and also what's okay as far as SE's policies go).

Take a look here and see what you can figure out: en.wikipedia.org/wiki/Fair_use ... @Antoni

@Glen_b Thanks. I couldn't be less concerned about lawyers affairs, but I do care a lot about intellectual ownership. I don't know if his proof is a standard derivation, or a completely original one. After all, anything to do with e should probably be credited to the number one, shouldn't it?

It was a question about the ethics, in other words, and I appreciate your answer. I think the legality is of no concern in this case.

It is a bit of an anticlimatic proof... It really strips the mystery away from the topic in a very expeditious way.

I was wondering if we have some (i.e., possibly under strict assumptions like existence of an underlying mgf) proof of the CLT on CV already? I have reviewed several posts on the CLT, but none of these had a proof. This is inspired by this: stats.stackexchange.com/questions/194327/… where OP asks about why to scale by $\sqrt{n}$ - something which I could not answer without a proof.

@user777 yea I thought of that too as a possible idea. Like approximate the derivative using the GP and then pass this information to your favorite local optimization algorithm like Newton-Rhapson, etc.

@RustyStatistician I'm not really sure it moves the ball forward any. You've still got to estimate GP parameters or make a model selection... But you're also essentially back to the problem of finding the point with the best EI or PI using the GP model as a surrogate.

@RustyStatistician and if you're being fully Bayesian, then you have many posterior models with many optima...