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imagine to have data like the following

$\begin{matrix}X1 & X2 & X3 \\\ 1 & 2 & 3\\\ 4 & 5 & 6\\\ 7 & 8 & 9\\\ \dots\end{matrix}$

where each row is a multivariate Gaussian (0, $\Sigma$).

Having the first order statistics for each column (mean, variance, median, min, max) + the covariance matrix, is it possible to get the third column knowing the other ones?

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  • $\begingroup$ Do you mean to ask if you can solve exactly for the third column? (unless the number of rows is very small) that is not possible. $\endgroup$ – kjetil b halvorsen Jan 30 at 3:26
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Do you mean to ask if you can solve exactly for the third column? Unless the number of rows is very small, or the covariance matrix $\Sigma$ is singular with a very specific structure, that is not possible.

You might be able to estimate the conditional distribution of the last column given the others, and simulate from that.

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