Convergence of Uniformity Criteria and the Application in Numerical Integration

Yang Huang and Yongdao Zhou ()
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Yang Huang: School of Statistics and Data Science, Nankai University, Tianjin 300071, China
Yongdao Zhou: School of Statistics and Data Science, Nankai University, Tianjin 300071, China

Mathematics, 2022, vol. 10, issue 19, 1-20

Abstract: Quasi-Monte Carlo (QMC) methods have been successfully used for the estimation of numerical integrations arising in many applications. In most QMC methods, low-discrepancy sequences have been used, such as digital nets and lattice rules. In this paper, we derive the convergence rates of order of some improved discrepancies, such as centered L 2 -discrepancy, wrap-around L 2 -discrepancy, and mixture discrepancy, and propose a randomized QMC method based on a uniform design constructed by the mixture discrepancy and Baker’s transformation. Moreover, the numerical results show that the proposed method has better approximation than the Monte Carlo method and many other QMC methods, especially when the number of dimensions is less than 10.

Keywords: Baker’s transformation; discrepancy; Quasi Monte Carlo (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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