I am trying to proof whether the SemiCovariance matrix defined in equation (5) from the following paper http://web.iese.edu/jestrada/PDF/Research/Refereed/MSO.pdf is positive definite or not.

As a starting point, I was thinking about using the whole covariance matrix, which is positive definite and then split it into the SemiCovariance and the rest. But from there I am stuck.

I appreciate your help.

Best, Jc

  • 1
    $\begingroup$ You might want to extract the relevant definition so that people don't have to open up the link. In general, the question should stand on its own. $\endgroup$
    – copper.hat
    May 27, 2015 at 16:46
  • $\begingroup$ covariance matrices are PSD since they can be written in the form $A^TA$, can something not be done similarly for the semi covariance matrix? $\endgroup$
    – Set
    May 27, 2015 at 16:49
  • $\begingroup$ Numerically, I am able to perform a Cholesky Factorization, but I have difficulties to visualize how this matrix looks like. $\endgroup$
    – Jonkie
    May 28, 2015 at 15:52


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