View abstract

Session I.7 - Stochastic Computation

Wednesday, June 14, 17:30 ~ 18:00

Mean estimation for Randomized Quasi Monte Carlo method

Emmanuel Gobet

Ecole polytechnique, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We are given a simulation budget of $B$ points to calculate an expectation $\mu=\mathbb{E}(F(U))$. A Monte Carlo method achieves a root mean squared risk of order $1/\sqrt B$, while a Randomized Quasi Monte Carlo (RQMC) method achieves an accuracy $\sigma_B \ll 1/\sqrt B$. The question we address in this work is, given a budget $B$ and a confidence level $\delta$, what is the optimal size of error tolerance such that $\mathbb{P}(|{\tt Est}-\mu| \gt {\tt TOL})\leq \delta$ for an estimator ${\tt Est}$ to be determined? We show that a judicious choice of ``robust'' aggregation methods coupled with RQMC methods allows to reach the best ${\tt TOL}$. This study is supported by numerical experiments, ranging from bounded $F(U)$ to heavy-tailed $F(U)$.

Joint work with Matthieu Lerasle ( CREST, ENSAE, Institut Polytechnique de Paris) and David Métivier (INRAE Montpellier).

View abstract PDF