Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence

Rémi Leluc, François Portier, Johan Segers () and Aigerim Zhuman
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Rémi Leluc: CMAP
François Portier: CREST
Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium
Aigerim Zhuman: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2025002, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: A novel linear integration rule called control neighbors is proposed in which nearest neighbor estimates act as control variates to speed up the convergence rate of the Monte Carlo procedure. The main result is the O(n−1/2n−1/d) convergence rate – where n stands for the number of evaluations of the integrand and d for the dimension of the domain – of this estimate for Lipschitz functions, a rate which, in some sense, is optimal. Several numerical experiments validate the complexity bound and highlight the good performance of the proposed estimator.

Keywords: Control variates; Hölder functions; metric space; Monte Carlo; nearest neighbor; optimal convergence rate; variance reduction; Voronoi cell (search for similar items in EconPapers)
Pages: 35
Date: 2025-03-01
Note: In: Bernoulli, 2025, vol. 31(2), p. 1160-1180
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2025002

DOI: 10.3150/24-BEJ1765

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