[R] R: ridge regression

[Liaw, Andy]

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.
>