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st: Adding a roughness penalty to the likelihood


From   Daniel.Koch@econhist.vwl.uni-muenchen.de
To   statalist@hsphsun2.harvard.edu
Subject   st: Adding a roughness penalty to the likelihood
Date   Mon, 13 Sep 2010 12:40:13 +0200 (CEST)

Dear all,
I would like to penalize my likelihood by either adding the integrated
second derivative of the of the regression function
or a penalty based on a difference-matrix of the coefficients to it.

More specifically:
The penalized log likelihood for the normal model should look something
like this:

`lnf' = (ln(normalden(($ML_y1 -`theta1')/`theta2')) -ln(`theta2')) +
$lambda*( `beta?*K*`beta_trans?)

With lambda being the smoothing parameter, K either being a matrix
consisting of the second derivatives or the differences and `beta? being
the evaluated coefficient-vector at this moment.

My question now is: How to I retrieve `beta??
?Theta? is giving me the linear combinations xb already evaluated but I
could not figure out how to get `beta? alone?

(At the moment  I interrupt the maximizing-process after each iteration
and use  e(b) of the last iteration as  `beta? for the next iteration. 
But this lagged `beta? is not correct I guess.)

Thanks a lot for your help.
Daniel


Dipl.-Volksw. Daniel Koch
Seminar für Wirtschaftsgeschichte
Ludwigstr.33 /IV
80539 München


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