Robust estimation with Randomized Quasi Monte Carlo
Séminaire Données et Aléatoire Théorie & Applications
24/03/2022 - 14:00 David Métivier (École Polytechnique) Salle 106
We are given a simulation budget of B points to calculate an expectation/integral. A Monte Carlo method achieves a mean squared error proportional to 1/B, while Randomized Quasi Monte Carlo methods are asymptotically faster. The question we address in this presentation is, given a budget B and some confidence level, what is the optimal confidence interval size one can build? For which estimator? We show that a judicious choice of "robust" aggregation methods coupled with Quasi Monte Carlo techniques allows to reach the optimal error bound. In this talk, I will present Quasi Monte Carlo methods, different concentration inequalities and robust mean estimators (old and new) to get to the solution, with supporting numerical experiments. This is a joint work with M. Lerasle and E. Gobet.