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Science Forum Index » Statistics - Math Forum » Uncorrelatedness implies independence (under what...
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 Posted: Wed Jun 25, 2008 11:07 am |
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Guest
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Columns of a matrix are uncorrelated. If I assume each column is
Gaussian distributed, can I say columns of the matrix are independent? |
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| ... |
| Posted: Wed Jun 25, 2008 11:17 am |
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On Jun 25, 5:07 pm, istillsh... at (no spam) gmail.com wrote:
Quote: Columns of a matrix are uncorrelated. If I assume each column is
Gaussian distributed, can I say columns of the matrix are independent?
I read the following two seemingly quite contradictory statements:
(1) If X and Y are uncorrelated and X and Y have normal distribution,
then X and Y are independent.
(2) It is possible for two random variables X and Y to be so
distributed jointly that each one is normally distributed, and they
are uncorrelated, but they are not independent. |
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| Ray Koopman... |
| Posted: Wed Jun 25, 2008 1:16 pm |
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On Jun 25, 2:07 pm, istillsh... at (no spam) gmail.com wrote:
Quote: Columns of a matrix are uncorrelated. If I assume each column is
Gaussian distributed, can I say columns of the matrix are independent?
Let W = +/- 1, each with probability 1/2, let X be standard normal
and independent of W, and let Y = W*X. Then Y is standard normal,
and X and Y are uncorrelated but are not independent. |
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| karl... |
| Posted: Wed Jun 25, 2008 4:57 pm |
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istillshine at (no spam) gmail.com schrieb:
Quote: On Jun 25, 5:07 pm, istillsh... at (no spam) gmail.com wrote:
Columns of a matrix are uncorrelated. If I assume each column is
Gaussian distributed, can I say columns of the matrix are independent?
I read the following two seemingly quite contradictory statements:
(1) If X and Y are uncorrelated and X and Y have normal distribution,
then X and Y are independent.
You have to cite precisely. This is wrong, 0nly if they have a JOINT
normal distribution it is true.
Quote: (2) It is possible for two random variables X and Y to be so
distributed jointly that each one is normally distributed, and they
are uncorrelated, but they are not independent.
Ciao
Karl |
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| Posted: Thu Jun 26, 2008 4:23 am |
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Guest
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On Jun 25, 5:07 pm, istillsh... at (no spam) gmail.com wrote:
Quote: Columns of a matrix are uncorrelated. If I assume each column is
Gaussian distributed, can I say columns of the matrix are independent?
Uncorrelated gaussian random variables are also independent, however,
this is not true for other distributions in genera.
Sangdon Lee |
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