EFFI

The theory of Local Asymptotic Mixed Normality provides a powerful framework under which we are able to discuss asymptotic optimality of estimators and tests of hypothesis for finite-dimensional parameters. When the (regular) LAMN property holds true for a statistical experiment, minimax theorems can be applied and a lower bound for the variance of the estimators can be derived. Moreover, the asymptotic power of a test of hypothesis can be evaluated by a computation under the null hypothesis. High-Frequency data has attracted attention due to their increasing availability in applications and have highlighted some statistical experiments where singularities are present. Namely, in such experiments, no minimax theorem can be applied and the asymptotic properties of the maximum likelihood estimator and the the likelihood ratio test of hypothesis are unknown. Moreover, the LAMN theory does not provide directly the construction of such efficient estimators or tests. The project aims to improve the knowledge on asymptotic efficiency for statistical experiments based on various stochastic processes and to provide new and innovative efficient estimators and tests for real applications in insurance and finance.