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Title: Regularized bridge-type estimation for SDEs Authors:  Alessandro De Gregorio - University of Rome La Sapienza (Italy) [presenting]
Abstract: The aim is to introduce an adaptive penalized estimator for identifying the true reduced parametric model under the sparsity assumption. In particular, we deal with the framework where the unpenalized estimator of the structural parameters needs simultaneously multiple rates of convergence (i.e., the so-called mixed-rates asymptotic behavior). We introduce a bridge-type estimator by taking into account penalty functions involving l-norms. We prove that the proposed regularized estimator satisfies the oracle properties. Our approach is useful for the estimation of stochastic differential equations in the parametric sparse setting. More precisely, under the high-frequency observation scheme, we apply our methodology to an ergodic diffusion and introduce a procedure for the selection of the tuning parameters. Furthermore, we will give some hints about possible future developments of this research topic.