Title: A unifying convex analysis framework to inference for penalized least squares
Authors: Alberto Quaini - University of Geneva (Switzerland) [presenting]
Fabio Trojani - USI (Switzerland)
Abstract: A unifying convex analysis framework is proposed for studying the properties of a broad class of Penalized Least Squares Estimators (PLSEs) with convex penalties. The basis of such framework is a reinterpretation of PLSEs as proximity operators evaluated at a Least Squares Estimator. Asymptotically, these operators converge under standard assumptions to a limit proximity operator evaluated at a Gaussian random vector, which is uniquely characterized by the limit penalty of a PLSE. We apply these characterizations to study with a unified approach the asymptotic bias functional of PLSEs, Oracle properties of PLSEs, valid bootstrap approximations for PLSEs' asymptotic distribution, and PLSEs with singular designs.