4
votes
Series of mutually independent variables that are dependent on an auxiliary random variable
Let $\{Y_i, i=1,2,\ldots, n\}$ be any finite collection of random variables for which
(i) $\{C\} \bigcup \{Y_i\}$ are independent and
(ii) $E[|Y_i|] \lt \infty$ for all $i.$
For $i=1, 2, \ldots,$ let $...
- 330k
4
votes
Accepted
Series of mutually independent variables that are dependent on an auxiliary random variable
If you want an actual example then it is easier to construct the $X_i$ first and then create $C$ depending on them.
For example, you could have $X_i \sim N(0,1)$ independently and have $C=2\Phi^{-1}\...
- 40.8k
1
vote
Gap between the given correlation parameter and the empirical correlation in (Gaussian) copula simulation
The value of linear correlations are not preserved across nonlinear transformation of the margins. The parameter, $\rho$ measures the Pearson correlation for a Gaussian copula when the margins are ...
- 287k
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