On Sun, 30 Jan 2011, David Winsemius wrote:
On Jan 30, 2011, at 6:02 AM, Alex Smith wrote:
Thank you for all your input but I'm afraid I dont know what the final
conclusion is. I will have to check the the eigenvalues if any are
negative. Why would setting them to zero make a difference? Sorry to
drag this on.
The discussion is proceeding on the assumption that the "true" matrix is
PD and that only because of numerical imprecision has a negative
eigenvalue been reported. You would only decide to set the negative
eigenvalues to zero if you had prior knowledge that the matrix _should_
be PD and that you needed to so something further with the matrix on
that basis. Usually the matrices in question are the result of many
calculations that may have introduced sufficient numerical round-off
error to distort the result.
In one common scenario you have computed variances and covariances
individually, then constructed a var-covar matrix from them. When the
true var-covar matrix was nearly singular, a matrix estimated in this way
can be negative definite because of different patterns of missing values
for different pairs of variables.
All true var-covar matrices are non-negative definite: They may be
singular (having at least one zero eigenvalue), but they cannot have a
negative eigenvalue.
Mike
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