Timeline for Zero covariance and independence
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2019 at 17:24 | comment | added | Han Chen | The multivariate Bernoulli distribution I referred is defined in Multivariate Bernoulli Distribution. In this paper, the equivalence has been proved. | |
| Oct 22, 2019 at 17:10 | comment | added | whuber♦ | It depends on which family of multivariate Bernoulli distributions you have in mind. There are families where uncorrelatedness does not imply independence. For instance, they might include the example in this answer where each pair of three Bernoulli variables is independent (and therefore uncorrelated) but the three variables are not independent. | |
| Oct 22, 2019 at 16:54 | comment | added | Han Chen | Thanks! I think I've found an example, multivariate Bernoulli distribution, which uncorrelatedness implies independence just like multivariate Normal distribution. | |
| Oct 21, 2019 at 21:23 | comment | added | whuber♦ | The general answer to your general question is any family of distributions in which the ones with zero covariance are also independent. Your reference to "prove" is a little mystifying, because you are asking only for characterizations. For the reasons I am giving, I consider this question to be overly broad: is there any way you can make it more specific? | |
| Oct 21, 2019 at 19:22 | comment | added | Han Chen | If you know that they are independent, then you don't need to prove independence. My question is, if we start from the joint pdf of some multivariate distribution and zero variance, under what kind of distribution can we reach to independence? multivariate normal is a common one, but what else? Multivariate t? | |
| Oct 21, 2019 at 19:11 | comment | added | whuber♦ | Sure, because you use the word "distribution" in the sense of a family of distributions. Any family whose members are all multivariate distributions of independent variables trivially has this property. Perhaps you intended to mean "distribution" in a more restrictive sense--but what would that be? | |
| Oct 21, 2019 at 19:05 | review | First posts | |||
| Oct 21, 2019 at 19:09 | |||||
| Oct 21, 2019 at 19:03 | history | asked | Han Chen | CC BY-SA 4.0 |