B0844
Title: Pathwise optimization for adaptive Bridge-type estimators: applications to stochastic differential equations
Authors: Francesco Iafrate - University of Rome La Sapienza (Italy) [presenting]
Abstract: The purpose is to study an adaptive penalized estimator for identifying the true reduced parametric model under structural sparsity assumptions. In particular, the framework where the unpenalized model parameter estimator simultaneously exhibits multiple convergence rates (i.e., the so-called mixed-rates asymptotic behaviour) is dealt with. A Bridge-type estimator is introduced by taking into account penalty functions involving $\ell^q$ norms (0 < q 1), which satisfies asymptotic oracle properties. A natural application of the multi-penalties approach is the estimation of stochastic differential equations in the parametric sparse setting. In real-world scenarios, the estimation task is challenging, especially for $0 < q < 1$, due to the non-convex nature of the optimization problem. Algorithms are studied that allow to efficiently compute the full solution path for penalized estimation methods as a function of the penalization parameter. Such algorithms rely on proximity operator-based non-convex analysis techniques. The methodology is applied to ergodic diffusion processes sampled under the high-frequency observation scheme, a common setting in financial applications. The estimation performance is analyzed on simulated and real data and compares the efficiency of several flavours of the algorithm, suggesting that some improvement in efficiency can be obtained by exploiting the block structure of the problem.
