What does this have to do with R? Is this homework? I suggest you post to some sort of math list. Perhaps others will have more specific suggestions where.
-- Bert On Thu, Dec 8, 2011 at 2:42 PM, Vivian Shih <v...@ucla.edu> wrote: > Hi, > > I've been trying to figure out a special set of covariance matrices that > causes some symmetric zero elements in the inverse covariance matrix but am > having trouble figuring out if that is possible. > > Say, for example, matrix a is a 4x4 covariance matrix with equal variance > and zero covariance elements, i.e. > > [,1] [,2] [,3] [,4] > [1,] 4 0 0 0 > [2,] 0 4 0 0 > [3,] 0 0 4 0 > [4,] 0 0 0 4 > > Now if we let a[1,2]=a[2,1]=3, then the inverse covariance matrix will > have nonzero elements on the diagonals as well as for elements [1,2] and > [2,1]. If we further let a[3,4]=a[4,3]=0.5 then the indices of the nonzero > elements of the covariance matrix also matches those indices of the inverse. > > The problem is, if any of the nonzero off-diagonal indices match, then > the inverse covariance matrix will have non-matching nonzero elements. For > example, if a[1,2]=a[2,1]=3 as before but now we'll let a[2,3]=a[3,2]=0.5, > then a would be: > > [,1] [,2] [,3] [,4] > [1,] 4 3.0 0.0 0 > [2,] 3 4.0 0.5 0 > [3,] 0 0.5 4.0 0 > [4,] 0 0.0 0.0 4 > > The inverse covariance matrix is now: > [,1] [,2] [,3] [,4] > [1,] 0.58333333 -0.44444444 0.05555556 0.00 > [2,] -0.44444444 0.59259259 -0.07407407 0.00 > [3,] 0.05555556 -0.07407407 0.25925926 0.00 > [4,] 0.00000000 0.00000000 0.00000000 0.25 > > If we let a[1,2] and a[2,3] be nonzero, then the inverse will create a > nonzero [1,3]. Does that happen all the time? I've tried to write out the > algebraic system of linear equations for a and a-inverse but couldn't come > up with anything. > > Let me know if I'm not clear on anything. Basically I'd just like to see > what type of covariance matrices will produce an inverse covariance matrix > with some zero elements. > > > > > > Thanks, > Vivian > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
