Quasiconcavity conjecture for marginal likelihoods of ridge, lasso, and group lasso

Let $Z(\lambda)$ denote the marginal likelihood for a regularized linear regression model, with ridge, lasso, and group lasso corresponding to their respective regularizers. Quasiconcavity conjecture. For each of these three models, $Z(\lambda)$ is a quasiconcave function. In other words, the empirical Bayes estimators for these models are conjectured to be expressed in the form presented in the theorem for the empirical Bayes regularized linear regression model. The claim is based on numerical calculations across the cases $m=n$, $m>n$, and $m<n$; no proof or resolution is supplied here.