Setting the negative eigenvalues (of which there may be many !) to zero
provides the least squares solution. Thus it gives \hat C such that
||C-\hat C||^2 is minimal over all psd matrices \hat C.
If C is a correlation matrix (as suggested below) then of course
C is already psd. If C is a matrix with merely diag(C)=I, then the
procedure above will usually not give diag(\hat C)=I.
At 14:57 -0500 07/06/2000, Rich Strauss wrote:
>At 03:46 PM 7/6/00 +0000, Christian A. Walter wrote:
>>Does anyone know if there is a structured way to adjust a negative
>>definite matrix such that it becomes semi-definite, while "minimizing"
>>the induced changes to the matrix?
>>
>>Cheers,
>>Christian
>
>I posed a similar question to edstat last fall. I was specifically
>concerned with non-positive-definite correlations matrices. Several people
>suggested to me the following numerical solution: get the eigenvectors and
>eigenvalues, set the negative eigenvalues to zero (there's generally only
>one that's negative) and proportionately adjust the others to maintain the
>same sum (total variance), and reconstruct the correlation matrix. This
>seems to work very well in practice. I've also done some simulations,
>beginning with a well-conditioned correlation matrix and gradually changing
>it until it becomes slightly ill-conditioned. The eigen procedure
>successfully 'corrects' the matrix.
>
>Rich Strauss
>
>
>
>
--
===
Jan de Leeuw; Professor and Chair, UCLA Department of Statistics;
US mail: 8142 Math Sciences Bldg, Box 951554, Los Angeles, CA 90095-1554
phone (310)-825-9550; fax (310)-206-5658; email: [EMAIL PROTECTED]
http://www.stat.ucla.edu/~deleeuw and http://home1.gte.net/datamine/
============================================================================
No matter where you go, there you are. --- Buckaroo Banzai
http://webdev.stat.ucla.edu/sounds/nomatter.au
============================================================================
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
