The sample covariance of N observations of K

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  • #1
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http://en.wikipedia.org/wiki/Covariance

I read from the above link that-

The sample covariance of N observations of K variables is the K-by-K matrix.

I am wondering-

Should "K-by-K" be "N-by-K" or not?
 

Answers and Replies

  • #2
mathman
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http://en.wikipedia.org/wiki/Covariance

I read from the above link that-

The sample covariance of N observations of K variables is the K-by-K matrix.

I am wondering-

Should "K-by-K" be "N-by-K" or not?
No. K-by-K is correct. Moreover it is symmetric. Each term in the matrix is the estimated covariance between two of the variables.
 
  • #3
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Does it mean covariance matrix must be in square size, 3x3, 4x4, 5x5 etc?

It can never be 3x4, 4x7, 5x8 etc.
Correct?
 
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  • #4
chiro
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Yes it has to be square. Remember that you need all possible values of Cov(X,Y) where X and Y are random variables. If you have N different variables then you have N*N or N^2 possibilities and since Cov(X,Y) = Cov(Y,X) you will have a lot of repeated values.
 
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  • #5
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you will have a lot of repeated values.
I think every value will repeat twice. Am I correct?
 
  • #6
chiro
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In general yes unless you are looking at the same random variable since Cov(X,X) = Var(X) on the diagonal elements.
 
  • #7
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Yes! I am just taking off diagonal elements into account.
 
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