Mean estimation for Randomized Quasi Monte Carlo method
Résumé
We are given a simulation budget of B points to calculate an expectation µ = E (F (U)). A Monte Carlo method achieves a root mean squared risk of order 1/ √ B, while a Randomized Quasi Monte Carlo method achieves an accuracy σ B 1/ √ B. The question we address in this work is, given a budget B and a confidence level δ, what is the optimal size of error tolerance such that P(|Est − µ| > TOL) ≤ δ for an estimator Est to be determined? We show that a judicious choice of "robust" aggregation methods coupled with RQMC methods allows to reach the best TOL. This study is supported by numerical experiments, ranging from bounded F (U) to heavy-tailed F (U).
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