[R] R: ridge regression

From: Clark Allan <Allan_at_stats.uct.ac.za>
Date: Wed 16 Feb 2005 - 21:58:33 EST

hi all

a technical question for those bright statisticians.

my question involves ridge regression.


n=sample size of a data set

X is the matrix of data with , say p variables

Y is the y matrix i.e the response variable

Z(i,j) = ( X(i,j)- xbar(j) / [ (n-1)^0.5* std(x(j))]

Y_new(i)=( Y(i)- ybar(j) ) / [ (n-1)^0.5* std(Y(i))] (note that i have scaled the Y matrix as well)

k is the ridge constant

the ridge estimate for the betas is = inverse(Z'Z+kI)*Z'Y_new=W*Z'Y_new

the associated variance covariance matrix sigma*W*(Z'Z)*W where sigma is the residual variance based on the transformed variables

if we transform the variables back to the original variables the beta estimates are now: beta(j)= std(y)*betaridge(j)/std(x(j))

but what is the covariance matrix of these estimates???

i know that this might not be the correct forum for this question, but since i know that many users are statisticians i know that i will get an informed response.

R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Feb 16 21:32:13 2005

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