dear all,

this question is regarding other possible applications of svd besides solving linear systems of equations. I'm interested in an efficient way to compute the Hat matrix from the svd of the model matrix (or at least its diagonal elements: hii) because these values are useful in linear modelling. Is it possible? This aspect is not covered in the book if I'm not wrong (neither it is for QR decomposition, for which a method exists; for instance, R uses the QR for computing hat values).

Many thanks

... I'm interested in an efficient way to compute the Hat matrix from the svd...

Check the following:

http://www.markirwin.net/stat221/Lecture/feb18.pdf

Bottom line:

If the SVD of matrix X is in the form

X = UDV^T



Then the hat matrix is

H = UU^T


It may or may not be the most computationally efficient way to get the hat matirx (SVD, in general is probably pretty expensive, computationally), but it's straightforward from the SVD.


Regards,

Dave