Covariance and Correlation

[bhfield]

I am replicating Rick's Covariance / Correlation Cholesky transformation within Proc IML as follows:

proc iml;

  D = { 1 2 3,

  2 4 3,

  3 3 9};

  X = root(D)`*root(D);

  print D;

  print X;

run;

Interestingly, X does not equal D.  I am wondering if this is due to D not being Positive Definite or, in other words, Det(D) <0.  The code runs without any indication of a problem.....had I not printed X, I would have never known that that Root(D)`*Root(D) would not equal D.

Any thoughts on why this is the case?

[Rick_SAS]

Interesting. I've never seen this behavior before. The correct behavior would be for the ROOT function to report an error in the log:

ERROR: (execution) Matrix should be positive definite

If I were to guess, I'd say that the exact integer values are causing a numerical problem in the ROOT function such that the ROOT function does not report the error. In the following code I perturb an element by a tiny amount and the ROOT function correctly reports that the matrix is not PD:

D[1] = D[1] + 1e-8;

G = root(D);

I will enter a bug report at SAS so that someone can look into this situation further.

[bhfield]

Thanks Dr. Wicklin.