Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models

Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models

It has been shown that AIC-type criteria are asymptotically efficient selectors of the tuning parameter in non-concave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regres...

Regularization parameter selection for penalized-maximum likelihood methods in PET

Penalized maximum likelihood methods are commonly used in positron emission tomography (PET). Due to the fact that a Poisson data-noise model is typically assumed, standard regularization parameter choice methods, such as the discrepancy principle or generalized cross validation, can not be directly applied. In recent work of the authors, regularization parameter choice methods for penalized ne...

Fast TV Regularization for 2D Maximum Penalized Likelihood Estimation

Total Variation-based regularization, well established for image processing applications such as denoising, was recently introduced for Maximum Penalized Likelihood Estimation (MPLE) as an effective way to estimate nonsmooth probability densities. While the estimates show promise for a variety of applications, the nonlinearity of the regularization leads to computational challenges, especially ...

Penalized Likelihood Estimation in Gaussian Mixture Models

Tuning Parameter Selection for Penalized Likelihood Estimation of Inverse Covariance Matrix

In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO penalty (Zou, 2006) have been proposed in literature. In this article, we establish the result that ...