Adaptive LASSO-type estimation for ergodic diffusion processes

The LASSO is a widely used statistical methodology for simultaneous estimation and variable selection. In the last years, many authors analyzed this technique from a theoretical and applied point of view. We introduce and study the adaptive LASSO problem for discretely observed ergodic diffusion processes. We prove oracle properties also deriving the asymptotic distribution of the LASSO estimator. Our theoretical framework is based on the random field approach and it applied to more general families of regular statistical experiments in the sense of Ibragimov-Hasminskii (1981). Furthermore, we perform a simulation and real data analysis to provide some evidence on the applicability of this method.