The question Confusion of central limit theory was asked recently. After I gave my answer, OP changed his/her question in a way that essentially makes my answer completely useless. In such situation, shall I delete my answer?
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12$\begingroup$ In this sort of situation, it might be preferable to roll OP's question back and ask him to open a new thread regarding his altered question. In any case, I don't think you should delete your answer. $\endgroup$– Stefan MeskenCommented Dec 22, 2016 at 15:00
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1$\begingroup$ @Stefan that's good advice in general, there can be however situations that are more complex. For example, in the current case there are also other answers that refer to the new version. $\endgroup$– quidCommented Dec 22, 2016 at 15:30
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$\begingroup$ @quid In a comment to your answer, I try to introduce the parameter "mathematical correctness" into this situation, since it seems to me to lead to different conclusions than the ones you suggest. $\endgroup$– DidCommented Dec 22, 2016 at 16:42
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As a rule a question should not be a moving target, and to alter it in such a way as to render existing answers wrong or even just incomplete is discouraged. It is alright to rollback such edits and to ask OP to ask a new question.
However, one should also strive to answer questions in the spirit in which they are asked, asking for clarifications first if needed.
I do not oversee all the details of the particular situation, but it appears that there was a poorly stated question and competing interpretations. By now the question is cleaned up and there is a satisfactory answer for OP.
In this case, yes, I think it could make sense to delete your answer. If you think there is lasting value in your answer, you could also add something to clarify its status and leave it around. Something like: "This answer refers to the original version of the question, and is intended to clarify some confusions."
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5$\begingroup$ Delving into "the details of the particular situation"... The question on main is the second installment by the same OP, obviously in search of some confirmation that unnormalized sums of i.i.d. increments can be said to be approximately normal in the sense that $$\sum_{i=1}^{M}X_{i}\to \mathcal{N}(M\mu,M\sigma^2)$$ This misconception was readily "confirmed" (alas), but it was also suitably dissected and the corresponding appropriate statement aptly explained. In such a context, I would chastise the edit of the question and certainly not recommend that this user (Jack) deletes their answer. $\endgroup$– DidCommented Dec 22, 2016 at 16:41
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$\begingroup$ Addendum: I forgot to mention that still another user (Gribouillis) posted an equally mathematically competent answer to the question. $\endgroup$– DidCommented Dec 22, 2016 at 16:47
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1$\begingroup$ Is the accepted answer false? If so what specific claim is false. You commented on it, but the comment does not make this readily apparent to me. Anyway, I still feel that the accepted answer takes a sane interpretation of the question. Gribouillis does not seem to have any particular problem with it either. Either way, I think there could be a version of the Q that allows for both (or rathr all three) answers to be meaningfully preserved, except the accepted answer is fundamentally false, but in this case you should be more explicit about this. $\endgroup$– quidCommented Dec 22, 2016 at 16:59
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$\begingroup$ It happens that the statement "the distribution function of $Y$ is close to the distribution function of $\text{N}(M\mu.M\sigma^2)$ everywhere" holds, but that it does not say what the OP thinks. To wit, for every fixed $x$, considering $Z_n$ normal $N(n\mu,n\sigma^2)$, $$P(Y_n\leqslant x)\to\ell\qquad P(Z_n\leqslant x)\to\ell$$ where $\ell=0$ if $\mu>0$, $\ell=\frac12$ if $\mu=0$ and $\ell=1$ if $\mu<0$. Hence, indeed, $$|P(Y_n\leqslant x)-P(Z_n\leqslant x)|\to0$$ just like, say, $$|P(Y_n\leqslant x)-P(T_n\leqslant x)|\to0$$ if each $T_n$ is Cauchy $(n\mu,0)$. :-) Let me add ... $\endgroup$– DidCommented Dec 22, 2016 at 17:11
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$\begingroup$ ... to conclude that all this is in fact re-playing a much played act, the need to get rid of false statements of the CLT being nearly as old as the CLT itself. $\endgroup$– DidCommented Dec 22, 2016 at 17:13
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1$\begingroup$ I am not an expert in this at all, but I reviewed the thing on main again, and I still feel that OP is somewhat entitled to the edits they made at least in part, especially given at what point that answer came in. Parts of that answer likely should have been given as a comment, in any case at that point. Specifically I am talking about the missing $M$ in the mean, which seems like a simple typo. I am not convinced we should force it to stay in OP only because a third answer puts focus on it. $\endgroup$– quidCommented Dec 22, 2016 at 17:33
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1$\begingroup$ The missing M factor is peripheral (even if Jack is quite right to mention it in their answer since such omissions are (again, classically) a source of confusion), the subject is the "limit" written as a displayed formula in my first comment. Re the timetable of events, the significant edit of the question (by user Arin Chaudhuri, later on "solidified" by EsJack) is posterior to all three answers currently posted, in particular Jack is right to state that "After (Jack) gave (their) answer, OP changed his/her question in a way that essentially makes (their) answer completely useless". $\endgroup$– DidCommented Dec 22, 2016 at 17:45
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1$\begingroup$ The other answers were already there though, which is what I said. The index $M$ to the $Y$ also seems a bit tangential of a subject to me. Then however, the question could be raised what relevant information this third answer adds over, say, the answer of Gribouillis. Anyway, my main point is that this specific example was not a completely usual instance of OP changed the question. As said, I think there could be a version of the question that allows for all answers to be preserved. $\endgroup$– quidCommented Dec 22, 2016 at 18:55
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1$\begingroup$ My meta post does not quite hit the mark, I might address this later, but I still feel that there is more to it in this case than only 'OP changed the question, and should not.' It is also not best practice to cement shortcomings of question posts when there are other options. But I do understand why OP of answer is unhappy about how things went too. Still, this answer also somewhat blasted into a thread that was already dealt with. I feel this changes the dynamic a bit. Would this answer been the first I'd see things differently. $\endgroup$– quidCommented Dec 22, 2016 at 19:02
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$\begingroup$ Surely you understood that I do not understand everything in your take on this, in particular I am not quite sure of the nature of the lessons you draw from the comparison to Griboullis' answer. To me, in the comments to Jack's answer: [You misunderstood the question, the OP is asking if YM is a good approximation to N(Mμ,Mσ2). Your edits have made the question nonsensical. – Arin Chaudhuri // I used every single word originally given by OP. You edited OP's question in your own way and criticized that my answer does not answer his question, which is unfair. – Jack // I apologize for ... $\endgroup$– DidCommented Dec 22, 2016 at 20:01
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$\begingroup$ ... my intemperate comments. I think my edits reflect the spirit of the original question better, I will let the OP decide. – Arin Chaudhuri], the first comment is difficult to excuse when one knows the sequence of events, whatever one thinks of the way the last comment mitigates it. Anyway, I shall be interested in reading your further thoughts on this, if you see fit to post any. $\endgroup$– DidCommented Dec 22, 2016 at 20:03
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1$\begingroup$ "in particular I am not quite sure of the nature of the lessons you draw from the comparison to Griboullis' answer." My point is that the point of Jack's answer is not quite clear to me. Moreover the style is questionable. I cannot help but have the impression the point was more to rip the question than to work towards a good thread. It's not out of line or anything, but the opening phrase does seem condescending, for example. I think a more supportive approached would have avoided the problem from the get go. $\endgroup$– quidCommented Dec 22, 2016 at 20:38
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1$\begingroup$ Generally, there is a longstanding and somewhat wide-spread problem with answerers focusing on minor problems or glitches with questions to have easily answerable questions rather than to work towards a meaningful question. Likely I am guilty of doing this myself sometimes.I am not certain this Q here is a case of that phenomenon, but the phenomenon exists. Some even do it unwittingly as they do not know better. Still others consider doing so as 'how things should be' But I don't. Not every change to a post is OP modifying the question, some are also OP clarifying the question. $\endgroup$– quidCommented Dec 22, 2016 at 20:44
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2$\begingroup$ ... on the only answer saying so and they agreed to the substantial change in their question supporting said answer. Again, AFAIK, the most important thing to explain here is why and how the statement $Y_M\to N(M\mu,M\sigma^2)$ is wrong, even if this is not what the OP wants to hear. $\endgroup$– DidCommented Dec 22, 2016 at 21:08
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1$\begingroup$ '(I disagree, and who is making assumptions now?' Uhm, you know the sentence you partially quoted started with "I think" and as such is clearly marked as a/my opinion (something that cannot be said about your " the edit was not a clarification, the OP wanted all along to hear that" ). I continue to think the answer could have been more constructive and it is not an optimal approach to focus in this form on "what is wrong." That's precisely my problem this exclusive, in part close to nit-picking, focus on what is wrong. $\endgroup$– quidCommented Dec 22, 2016 at 22:43