Variance of quadrature over scrambled unions of nets

Statistica Sinica

Volumn 9, Issue 2, 1999, Pages 451-473

  Yue, Rong Xian ^a,b  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

Integration; Multiresolution; Quasi Monte Carlo

Indexed keywords

EID: 0033469635     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. Daubechies, I. (1992). Ten Lectures on Wavelets. CBMS-NSF, SIAM, Philadelphia.
2. Efron, B. and Stein, C. (1981). The jackknife estimate of variance. Ann. Statist. 9, 586-596.
3. Fang, K. T. and Wang, Y. (1994). Number-Theoretic Methods in Statistics. Chapman and Hall, London.
4. Hickernell, F. J. (1996). Quadrature error bounds with applications to lattice rules. SIAM J. Num. Anal. 33, 1995-2016.
5. Hickernell, F. J. (1998). A generalized discrepancy and quadrature error bound. Math. Comp. 67, 229-322.
6. Hua, L. K. and Wang, Y. (1981). Applications of Number Theory to Numerical Analysis. Springer Verlag, Berlin.
7. Jawerth, B. and Sweldens, W. (1994). An overview of wavelet based multiresolution analyses. Technical Report, Department of Mathematics, University of South Carolina.
8. m). In Wavelets: A Tutorial in Theory and Applications (Edited by C. K. Chui). Academic Press, New York.
9. Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia.
10. Owen, A. B. (1992). Randomized orthogonal arrays for computer experiments, integration and visualization. Statist. Sinica 2, 439-452.
11. Owen, A. B. (1995). Randomly permuted (t, m, s)-nets and (t, s)-sequences. In Monte Carlo and Quoasi-Monte Carlo Methods in Scientific Computing (Edited by H. Niederreiter and P. J. S. Shiue), 299-317. Lecture Notes in Statistics, Vol. 106, Springer-Verlag, Berlin.
12. Owen, A. B. (1997a). Monte Carlo variance of scrambled equidistribution quadrature. SIAM, J. Num. Anal. 34, 1884-1910.
13. Owen, A. B. (1997b). Scrambled net variance for integrals of smooth functions. Ann. Statist. 25, 1541-1562.
14. Owen, A. B. (1998). Scrambled Sobol and Niederreiter-Xing points. J. Complexity 14, 466-489.
15. Sloan, I. H. and Joe, S. (1994). Lattice Methods for Multiple Integration. Clarendon Press, Oxford.
16. Wahba, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.