On the variance of quadrature over scrambled nets and sequences

DOI10.1016/S0167-7152(99)00018-8zbMath0970.65006WikidataQ127658625 ScholiaQ127658625MaRDI QIDQ1962204

Rong-Xian Yue, Shisong Mao

Publication date: 12 June 2001

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

Monte Carlo methodsMonte Carlo integration\((t,s)\)-sequence\((t,m,s)\)-netequidistribution methods

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

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Preintegration via Active Subspace ⋮ Integration and approximation based on scramble sampling in arbitrary dimensions ⋮ Strong tractability of integration using scrambled Niederreiter points ⋮ On integration methods based on scrambled nets of arbitrary size ⋮ My dream quadrature rule ⋮ The nonzero gain coefficients of Sobol's sequences are always powers of two ⋮ On Dropping the First Sobol’ Point ⋮ Improved bounds on the gain coefficients for digital nets in prime power base ⋮ A construction of polynomial lattice rules with small gain coefficients ⋮ On the asymptotic distribution of scrambled net quadrature. ⋮ Unnamed Item ⋮ Optimal quadrature for Haar wavelet spaces ⋮ The discrepancy and gain coefficients of scrambled digital nets.

Cites Work

• The jackknife estimate of variance
• Scrambling Sobol' and Niederreiter-Xing points
• Scrambled net variance for integrals of smooth functions
• Monte Carlo Variance of Scrambled Net Quadrature
• Quadrature Error Bounds with Applications to Lattice Rules
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