Timeline for On the assumptions in the Berry-Esseen Theorem
Current License: CC BY-SA 3.0
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| Mar 14, 2016 at 16:32 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Mar 14, 2016 at 15:46 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Mar 14, 2016 at 14:52 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Mar 14, 2016 at 14:34 | comment | added | Iosif Pinelis | Alas, your reformulation has not improved the question. With $ES_n^2=1$ and $E|X_1|^3=b$, the Berry--Esseen bound is $cnb$ (not $cb/\sqrt n$), and (in view, say, of the Edgeworth expansion) the factor $n$ in $cnb$ cannot be improved under any moment finiteness condition. Also, as long as you assume $ES_n^2=1$, you cannot say "we fix the distribution [of $X_1$]" -- because then $EX_1^2=1/n$, which depends on $n$. I still don't see a meaningful reinterpretation of the question other than the one given in my answer. | |
| Mar 14, 2016 at 5:56 | comment | added | TOM | This is indeed a useful comment and I will mend the formulation. Yet it is not what I exactly mean, although very close. This time I am sure that it is more meaningful. | |
| Mar 14, 2016 at 4:41 | history | answered | Iosif Pinelis | CC BY-SA 3.0 |