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Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence

Author

Listed:
  • Leluc, Rémi

    (CMAP)

  • Portier, François

    (CREST)

  • Segers, Johan

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Zhuman, Aigerim

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

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.

Suggested Citation

  • Leluc, Rémi & Portier, François & Segers, Johan & Zhuman, Aigerim, 2025. "Speeding up Monte Carlo Integration: Control Neighbors for Optimal Convergence," LIDAM Reprints ISBA 2025002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2025002
    DOI: https://doi.org/10.3150/24-BEJ1765
    Note: In: Bernoulli, 2025, vol. 31(2), p. 1160-1180
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    Cited by:

    1. Patilea, Valentin & Wang, Sunny G․ W․, 2026. "Rate accelerated inference for integrals of multivariate random functions," Computational Statistics & Data Analysis, Elsevier, vol. 214(C).

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