On the existence of the weighted bridge penalized Gaussian likelihood precision matrix estimator

We establish a necessary and sufficient condition for the existence of the precision matrix estimator obtained by minimizing the negative Gaussian log-likelihood plus a weighted bridge penalty. This condition enables us to connect the literature on Gaussian graphical models to the literature on penalized Gaussian likelihood.Fil: Rothman, Adam J.. University of Minnesota. Scool Of Statistics; Estados UnidosFil: Forzani, Liliana Maria. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Santa Fe. Instituto de Matemática Aplicada "Litoral"; Argentin