[R] R: ridge regression

[Clark Allan]

hi Andy and other r users

i never gave the full picture. 

beta(j)= std(y)*betaridge(j)/std(x(j))	for j=1,2,...p

but beta(0) = ybar- sum( i= 1 to p, betaridge(i)*xbar(j) )

note that ybar and the xbars are estimated parameters.

we can split the covariance matrix into three sections namely:

1. var(beta(0))
2. covar(beta(0), other betas) and
3. covar(other betas)	, (this is your answer, which was correct)

but now i need var(beta(0)) and covar(beta(0), other betas)

any suggestions!




"Liaw, Andy" wrote:
> 
> If I'm not mistaken, you only need to know that if V is the covariance
> matrix of a random vector X, then the covariance of the linear
> transformation AX + b is AVA'.  Substitute betahat for X, and figure out
> what A is and you're set.  (b is 0 in your case.)
> 
> Andy
> 
> > From: Clark Allan
> >
> > 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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