  This paper extends some prominent statistical results including \emph{Fisher
Theorem and Wilks phenomenon} to the penalized maximum likelihood estimation
with a quadratic penalization. It appears that sharp expansions for the
penalized MLE \(\tilde{\thetav}_{G} \) and for the penalized maximum likelihood
can be obtained without involving any asymptotic arguments, the results only
rely on smoothness and regularity properties of the of the considered
log-likelihood function. The error of estimation is specified in terms of the
effective dimension \(p_G \) of the parameter set which can be much smaller
than the true parameter dimension and even allows an infinite dimensional
functional parameter. In the i.i.d. case, the Fisher expansion for the
penalized MLE can be established under the constraint "\(p_G^{2}/n\) is small"
while the remainder in the Wilks result is of order \(p_G^{3}/n \).
