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A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study stability properties of the penalized maximum likelihood estimator, two types of asymptotic stability are defined. Theoretical properties, including the parameter estimation consistency, model selection consistency, and asymptotic stability, are established under suitable regularity conditions. An efficient coordinate-descent algorithm is proposed. Simulation results and real data analysis show that the proposed method has competitive performance in comparison with existing ones.
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the rea
We derive Laplace-approximated maximum likelihood estimators (GLAMLEs) of parameters in our Graph Generalized Linear Latent Variable Models. Then, we study the statistical properties of GLAMLEs when the number of nodes $n_V$ and the observed times of
The maximum likelihood estimator plays a fundamental role in statistics. However, for many models, the estimators do not have closed-form expressions. This limitation can be significant in situations where estimates and predictions need to be compute
Suppose an online platform wants to compare a treatment and control policy, e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site. Standard randomized controlled tri
Statistical models with latent structure have a history going back to the 1950s and have seen widespread use in the social sciences and, more recently, in computational biology and in machine learning. Here we study the basic latent class model propo