How to calculate the covariance matrix?

Question

I tried searching a lot on the net and got the following sources: http://stattrek.com/matrix-algebra/covariance-matrix.aspx http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm The first source seems to be incorrect cause when I calculate it using matlab it comes to be different from what they have given as the answer. As for the second link I cant understand that cause its not completely explaining as to how to calculate. Could anyone please provide me with a sound link or explain how to calculate a co-variance matrix?

Answer 1

Do you mean interpret the covariance matrix or do you mean calculate the covariance matrix?

To interpret the covariance matrix you have a column for each variable and a row for each variable the Cov( X_i , X_j) corresponds to the entry in ith row and jth column of your matrix. This will be the same value as Cov(X_j, X_i) which is the jth row and ith column of your matrix. The Cov (X_i,X_i) = Var (X_i) . This means to covariance between the same variable is equal to the variance of that variable.

To find the covariance matrix you need to calculate the Fisher information matrix. You will need to take the partial derivatives of the Maximum Likelihood Estimate and take the expected value of that to find the Information Matrix. I think if you gave an example it would be easier to help you with the problem you are having.