Walsh functions, scrambled $(0, m, s)$-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration

@article{Wiart2021WalshFS,
  title={Walsh functions, scrambled \$(0, m, s)\$-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration},
  author={Jaspar Wiart and Elaine Wong},
  journal={Math. Comput. Simul.},
  year={2021},
  volume={182},
  pages={277-295}
}
Abstract We investigate base b Walsh functions for which the variance of the integral estimator based on a scrambled ( 0 , m , s ) -net in base b is less than or equal to that of the Monte-Carlo estimator based on the same number of points. First we compute the Walsh decomposition for the joint probability density function of two distinct points randomly chosen from a scrambled ( t , m , s ) -net in base b in terms of certain counting numbers and simplify it in the special case t is zero. Using… Expand
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