Mean estimation for Randomized Quasi Monte Carlo method

Emmanuel Gobet (1) , Matthieu Lerasle (2) , David Métivier (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Centre de Recherche en Économie et STatistique (CREST)

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).

Mots clés: robust statistics; Quasi Monte Carlo methods; PAC bounds

Domaines: Probabilités [math.PR]; Théorie [stat.TH]

Emmanuel Gobet, Matthieu Lerasle, David Métivier. Mean estimation for Randomized Quasi Monte Carlo method. 2022. ⟨hal-03631879v2⟩