Timeline for Dependence rank: what is the size of the largest subcollection of random variables which is statistically independent?
Current License: CC BY-SA 4.0
9 events
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| Apr 27, 2020 at 23:10 | comment | added | dohmatob | It was a problem with terminology. Removed the "pairwise" adjective. | |
| Apr 27, 2020 at 23:09 | history | edited | dohmatob | CC BY-SA 4.0 |
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| Apr 27, 2020 at 21:14 | comment | added | Jeppe Stig Nielsen | Recall that for $k\ge 3$, pairwise independence is weaker than full ("mutual") independence. What is your motivation for using "pairwise" in your definition? | |
| Apr 27, 2020 at 19:57 | history | edited | dohmatob | CC BY-SA 4.0 |
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| Apr 27, 2020 at 19:57 | comment | added | dohmatob | Yes, indeed covarance matrices don't capture nonlinear dependence patterns. Removed my comment above cov matrix. | |
| Apr 27, 2020 at 19:40 | history | edited | dohmatob | CC BY-SA 4.0 |
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| Apr 27, 2020 at 19:16 | comment | added | user44143 | I don't think you can say much from the covariance matrix. Consider a) $X$ and $Y$ independent uniform variables on $[-1,1]$, or b) $X$ as before, $Y = 2|X|$. They have the same covariance matrix but a) has rank 2 and b) has rank 1. | |
| Apr 27, 2020 at 18:57 | history | edited | dohmatob | CC BY-SA 4.0 |
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| Apr 27, 2020 at 18:51 | history | asked | dohmatob | CC BY-SA 4.0 |