Chicago Booth, USA
Title: Inference in high-dimensional nonparametric graphical models
Abstract: In this talk, we discuss root-n consistent estimators for elements of the latent precision matrix under high-dimensional elliptical copula models. Under mild conditions, the estimator is shown to be asymptotically normal, which allows for construction of tests about presence of edges in the underlying graphical model. The asymptotic distribution is robust to model selection mistakes and does not require non-zero elements to be separated away from zero. The key technical result is a new lemma on the “sign-subgaussian” property, which allows us to establish optimality of the estimator under the same conditions as in the gaussian setting. Extension to dynamic elliptical copula models will also be presented.
Joint work with Rina Foygel Barber, Junwei Lu, and Han Liu.