A1685
Title: Flexible regularized estimating equations: Some new perspectives
Authors: Archer Yang - McGill University (Canada) [presenting]
Abstract: Some observations about the equivalences between regularized estimating equations, fixed-point problems and variational inequalities are made: (a) A regularized estimating equation is equivalent to a fixed-point problem, specified via the proximal operator of the corresponding penalty; (b) A regularized estimating equation is equivalent to a (generalized) variational inequality. Both equivalences can extend to any estimating equations with nonconvex penalty functions. To solve large-scale regularized estimating equations, it is worth pursuing computation by exploiting these connections. While fast computational algorithms are less developed for regularized estimating equations, there are many efficient solvers for fixed-point problems and variational inequalities. In this regard, we apply some efficient and scalable solvers which can deliver a hundred-fold speed improvement. These connections can lead to further research in both computational and theoretical aspects of the regularized estimating equations. We will also discuss applications of our approach in dynamic treatment regimes, instrumental variable regression and generalized estimation equations.
