hi all

a technical question for those bright statisticians.

my question involves ridge regression.

definition:

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.

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