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<p>In randomized quasi-Monte Carlo methods for numerical integration, average estimators based on digital nets with fully nested and linear scramblings, respectively, are known to exhibit the same variance. In this note, we show that this equivalence does not extend to the median estimators. Specifically, while the median estimator with linear scrambling can achieve faster convergence for smooth integrands, the median estimator with fully nested scrambling does not exhibit this advantage.</p>

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The median trick does not help for fully nested scrambling

  • 期刊论文

  • 发表日期：

    2025年11月26日

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  • Takashi Goda,
  • Kosuke Suzuki

摘要

In randomized quasi-Monte Carlo methods for numerical integration, average estimators based on digital nets with fully nested and linear scramblings, respectively, are known to exhibit the same variance. In this note, we show that this equivalence does not extend to the median estimators. Specifically, while the median estimator with linear scrambling can achieve faster convergence for smooth integrands, the median estimator with fully nested scrambling does not exhibit this advantage.