Timeline for Convergence in probability of sample covariance for permutation invariant triangular arrays
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
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| Jun 13 at 23:19 | vote | accept | Greg Zitelli | ||
| Jun 10 at 21:11 | answer | added | Iosif Pinelis | timeline score: 1 | |
| Jun 10 at 11:39 | comment | added | Iosif Pinelis | Yes. I am still trying to find time to write the answer. | |
| Jun 10 at 6:37 | comment | added | Greg Zitelli | @IosifPinelis permutation invariant is enough to show the whole result? You mean without the assumptions on higher moments? | |
| Jun 9 at 1:13 | history | edited | Greg Zitelli | CC BY-SA 4.0 |
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| Jun 7 at 3:29 | comment | added | Iosif Pinelis | I think "permutation invariant" is enough. I will try to find time to write this up. | |
| Jun 7 at 2:24 | comment | added | Iosif Pinelis | "permutation invariant" should have been stated in the original version of your post. | |
| Jun 7 at 2:01 | comment | added | Greg Zitelli | @IosifPinelis there are no other conditions missing. Permutation invariant is defined in the first bullet, is it not clear? | |
| Jun 7 at 1:50 | comment | added | Iosif Pinelis | "permutation invariant"? What other conditions are missing here? (I asked this in my first comment on this page.) | |
| Jun 7 at 1:44 | history | edited | Greg Zitelli | CC BY-SA 4.0 |
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| Jun 7 at 1:35 | comment | added | Greg Zitelli | Since it seems confusing I will remove the last part I suppose... I made it clear that the random variables are not iid but are permutation invariant. | |
| Jun 7 at 1:34 | history | edited | Greg Zitelli | CC BY-SA 4.0 |
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| Jun 6 at 20:38 | comment | added | Iosif Pinelis | I don't understand the equality in your last last display, nor do I know what conditions you are assuming there. Again, are the $X_{N,i}$' s iid? Are the $Y_{N,i}$' s iid? Also, and more importantly, why do you think the convergence of the expected values would imply the convergence in probability?? | |
| Jun 6 at 19:44 | comment | added | Greg Zitelli | Rephrased and tried to clarify further. | |
| Jun 6 at 19:43 | history | edited | Greg Zitelli | CC BY-SA 4.0 |
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| Jun 6 at 19:12 | comment | added | Iosif Pinelis | Are $x_{N,1},\dots,x_{N,N},y_{N,1},\dots,y_{N,N}$ random variables? Are $x_{N,1},\dots,x_{N,N},y_{N,1},\dots,y_{N,N}$ jointly independent? Are the $x_{N,i}$'s iid? Are the $y_{N,i}$'s iid? Any other conditions missing? How is it "easy to show"? | |
| Jun 6 at 18:40 | comment | added | Greg Zitelli | @DieterKadelka clarified. | |
| Jun 6 at 18:39 | history | edited | Greg Zitelli | CC BY-SA 4.0 |
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| Jun 6 at 18:24 | comment | added | Dieter Kadelka | I don't understand. What are precisely the assumptions? First, the $x_{N,i}$, $y_{N,i}$ need not be independent? 2. Good measure? 3. $a_n$, $b_n$ finite? 4. $\mathbb{E}|x_{N,i}| = \infty$? $\ldots$ | |
| Jun 6 at 17:24 | history | edited | Greg Zitelli | CC BY-SA 4.0 |
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| Jun 6 at 16:21 | history | asked | Greg Zitelli | CC BY-SA 4.0 |