Mixing
Formula for the cross covariance of sums of random vectors?
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Is there a general formula for the cross covariance for sums of random vectors?
Let $A = sum_{i=1}^nc_iX_i$ where each $X_i$ is an $n$-dimensional random vector.
Let $B = sum_{j=1}^n b_jY_j$ be defined similarly.
Is there a formula for $text{Cov}(A,B)$?
And for the special case assuming that each $X_i,Y_i$ has mean and covariance $mu$ and $Sigma$, respectively. What does this reduce to?
I'm assuming it's something of the form:
$sum_{i=1}^nsum_{j=1}^n c_ib_itext{Cov($X_i, Y_i$)}$, but I'm not entirely sure.
linear-algebra statistics definition
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
$endgroup$
add a comment |
$begingroup$
Is there a general formula for the cross covariance for sums of random vectors?
Let $A = sum_{i=1}^nc_iX_i$ where each $X_i$ is an $n$-dimensional random vector.
Let $B = sum_{j=1}^n b_jY_j$ be defined similarly.
Is there a formula for $text{Cov}(A,B)$?
And for the special case assuming that each $X_i,Y_i$ has mean and covariance $mu$ and $Sigma$, respectively. What does this reduce to?
I'm assuming it's something of the form:
$sum_{i=1}^nsum_{j=1}^n c_ib_itext{Cov($X_i, Y_i$)}$, but I'm not entirely sure.
linear-algebra statistics definition
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
$endgroup$
add a comment |
$begingroup$
Is there a general formula for the cross covariance for sums of random vectors?
Let $A = sum_{i=1}^nc_iX_i$ where each $X_i$ is an $n$-dimensional random vector.
Let $B = sum_{j=1}^n b_jY_j$ be defined similarly.
Is there a formula for $text{Cov}(A,B)$?
And for the special case assuming that each $X_i,Y_i$ has mean and covariance $mu$ and $Sigma$, respectively. What does this reduce to?
I'm assuming it's something of the form:
$sum_{i=1}^nsum_{j=1}^n c_ib_itext{Cov($X_i, Y_i$)}$, but I'm not entirely sure.
linear-algebra statistics definition
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
$endgroup$
Is there a general formula for the cross covariance for sums of random vectors?
Let $A = sum_{i=1}^nc_iX_i$ where each $X_i$ is an $n$-dimensional random vector.
Let $B = sum_{j=1}^n b_jY_j$ be defined similarly.
Is there a formula for $text{Cov}(A,B)$?
And for the special case assuming that each $X_i,Y_i$ has mean and covariance $mu$ and $Sigma$, respectively. What does this reduce to?
I'm assuming it's something of the form:
$sum_{i=1}^nsum_{j=1}^n c_ib_itext{Cov($X_i, Y_i$)}$, but I'm not entirely sure.
linear-algebra statistics definition
linear-algebra statistics definition
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
asked Jan 28 at 19:19
Oliver GOliver G
1,3651632
1,3651632
add a comment |
add a comment |
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