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The sample covariance of N observations of K

  1. Sep 11, 2013 #1
    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?
     
  2. jcsd
  3. Sep 11, 2013 #2

    mathman

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    No. K-by-K is correct. Moreover it is symmetric. Each term in the matrix is the estimated covariance between two of the variables.
     
  4. Sep 11, 2013 #3
    Does it mean covariance matrix must be in square size, 3x3, 4x4, 5x5 etc?

    It can never be 3x4, 4x7, 5x8 etc.
    Correct?
     
    Last edited: Sep 12, 2013
  5. Sep 12, 2013 #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.
     
  6. Sep 12, 2013 #5
    I think every value will repeat twice. Am I correct?
     
  7. Sep 12, 2013 #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.
     
  8. Sep 12, 2013 #7
    Yes! I am just taking off diagonal elements into account.
     
    Last edited: Sep 12, 2013
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