Penalized maximum likelihood estimation and effective dimension

Understand

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.