Abstract
There have been few studies on practical error estimation methods of quasi-Monte Carlo integrations. Recently, some theoretical works were developed by Owen to analyze the quasi-Monte Carlo integration error. However his method given by those works is complicated to be implemented and needs huge computational efforts, so it would be of some interest to investigate into a simple error estimation method. In this paper, we will use a simple method, and give some theoretical considerations on the errors given by these two methods. Numerical experiments are also reported.
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References
Cranley, R. and T. N. L. Patterson: Randomization of Number Theoretic Methods for Multiple Integration.SIAM J. Numer. Anal., Vol. 13, No. 6, pp. 904–914, 1976.
Entacher, K.: Quasi-Monte Carlo Methods for Numerical Integration of Multivariate Haar Series.BIT, Vol. 37, No. 4, pp. 846–861, 1997.
Genz, A.: Testing Multidimensional Integration Routines. InTools, Methods and Languages for Scientific and Engineering Computation, B. Ford, J. C. Rault, F. Thomasset (editors), pp. 81–94, North-Holland, 1984.
Niederreiter, H.:Random Number Generation and Quasi-Monte Carlo Methods. CBMS-NSF Regional Conference Series in Applied Mathematics No.63, SIAM, 1992.
Okten, G.: Error Estimation for Quasi-Monte Carlo Methods. InMonte Carlo and Quasi-Monte Carlo Methods 1996, H. Niederreiter, P. Hellekalek, G. Larcher, and P. Zinterhof(editors), LNS 127, pp. 353–368, Springer, 1998.
Owen, A. B.: Monte Carlo Variance of Scrambled Equidistribution Quadrature.SIAM J. Numer. Anal., Vol. 34, No. 5, pp. 1884–1910, 1997.
Owen, A. B.: Scrambled Net Variance for Integrals of Smooth Functions.Ann. Statist., Vol. 25, No. 4, pp. 1541–1562, 1997.
Tuffin, B.: On the Use of Low Discrepancy Sequences in Monte Carlo Methods. Technical Report No. 1060, IRISA, Rennes, 1996.
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Morohosi, H., Fushimi, M. (2000). A Practical Approach to the Error Estimation of Quasi-Monte Carlo Integrations. In: Niederreiter, H., Spanier, J. (eds) Monte-Carlo and Quasi-Monte Carlo Methods 1998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59657-5_26
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DOI: https://doi.org/10.1007/978-3-642-59657-5_26
Publisher Name: Springer, Berlin, Heidelberg
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