MCQMC methods for multivariate statistical distributions

Monte Carlo and Quasi-Monte Carlo Methods 2006

Volumn , Issue , 2008, Pages 35-52

  Genz, Alan ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MULTIVARIANT ANALYSIS;

MONTE CARLO AND QUASI-MONTE CARLO METHODS; MULTIVARIATE NORMAL; MULTIVARIATE T DISTRIBUTION; PROBLEM FORMULATION; QUASI MONTE CARLO METHODS; RANDOMIZED QUASI MONTE CARLO METHODS; SEPARATION OF VARIABLES; STATISTICAL DISTRIBUTION;

MONTE CARLO METHODS;

EID: 72449151016     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-74496-2_3     Document Type: Conference Paper

References (37)

1. [BH92] M. Beckers and A. Haegemans. 'Comparison of Numerical Integration Techniques for Multivariate Normal Integrals', Computer Science Department Preprint, Catholic University of Leuven, Belgium, 1992.
2. [Co54] E. A. Cornish. 'The Multivariate t-Distribution Associated with a Set of Normal Sample Deviates', Australian Journal of Physics 7, pp. 531-542, 1954.
3. [De80] I. Deák. 'Three Digit Accurate Multiple Normal Probabilities' Numer. Math. 35, pp. 369-380, 1980.
4. [De86] I. Deák. 'Computing Probabilities of Rectangles in Case of Multinormal Distribution' J. Statist. Comput. Simul. 26, pp. 101-114, 1986.
5. [De90] I. Deák. Random Number Generation and Simulation, Akadémiai Kiado, Budapest, Chapter 7, 1990.
6. [Dv86] L. Devroye. 'Non-Uniform Random Variate Generation' Springer-Verlag, Berlin, 1986.
7. [FW94] K.-T. Fang and Y. Wang. Number-Theoretic Methods in Statistics, Chapman and Hall, London, pp. 167-170, 1994.
8. [GDS02] H. I. Gassmann, I. Deák, and T. Szántai. 'Computing Multivariate Normal Probabilities: a New Look', J. Comp. Graph. Stat. 11, pp. 920-949, 2002.
9. [Ge92] A. Genz. 'Numerical Computation of the Multivariate Normal Probabilities', J. Comput. Graph. Stat. 1, pp. 141-150, 1992.
10. [Ge93] A. Genz. 'A Comparison of Methods for Numerical Computation of Multivariate Normal Probabilities', Computing Science and Statistics 25, pp. 400-405, 1993.
11. [GB99] A. Genz and F. Bretz. Numerical Computation of Multivariate t Probabilities with Application to Power Calculation of Multiple Contrasts, J. Stat. Comp. Simul. 63, pp. 361-378, 1999.
12. [GB00] A. Genz and F. Bretz. 'Numerical Computation of Critical Values for Multiple Comparison Problems', in Proceedings of the Statistical Computing Section, American Statistical Association, Alexandria, VA, pp. 84-87, 2000.
13. [GB01] A. Genz and F. Bretz. 'Critical Point and Power Calculations for the Studentised Range Test', J. Stat. Comp. Simul. 71, pp. 85-97, 2001.
14. [GB02] A. Genz and F. Bretz. 'Comparison of Methods for the Computation of Multivariate t Probabilities', J. Comp. Graph. Stat. 11, pp. 950-971.
15. [GK99] A. Genz and K. S. Kwong. 'Numerical Evaluation of Singular Multivariate Normal Distributions', J. Stat. Comp. Simul. 68, pp. 1-21, 1999.
16. [Ge91] J. Geweke. 'Efficient Simulation from the Multivariate Normal and Student-T Distributions Subject to Linear Constraints', Computing Science and Statistics 23, pp. 571-578, 1991.
17. [GG94] G. J. Gibson, C. A. Glasbey, and D. A. Elston. 'Monte-Carlo Evaluation of Multivariate Normal Integrals and Sensitivity to Variate Ordering', in Proceedings of the Third International Conference in Numerical Methods and Applications, World Scientific, Singapore, pp. 120-126, 1994.
18. [Ha93] V. Hajivassiliou. 'Simulating Normal Rectangle Probabilities and Their Derivatives: The effects of Vectorization', The International Journal of Supercomputer Applications 7, pp. 231-253, 1993.
19. [HMR96] V. Hajivassiliou, D. McFadden, and O. Rudd. 'Simulation of Multivariate Normal Rectangle Probabilities and Their Derivatives: Theoretical and Computational Results', Journal of Econometrics, 72, pp. 85-134, 1996
20. [HH97] F. J. Hickernell and H. S. Hong. 'Computing Multivariate Normal Probabilities Using Rank-1 Lattice Sequences', in Proceedings of the Workshop on Scientific Computing (Hong Kong), (G. H. Golub, S. H. Lui, F. T. Luk, and R. J. Plemmons, eds.), Springer-Verlag, Singapore, pp. 209-215, 1997.
21. [HHLL00] F. J. Hickernell, H. S. Hong, P. L'Ecuyer, and C. Lemieux. 'Extensible Lattice Sequences for QMC Quadrature' SIAM Journal of Scientific and Statistical Computing 22, pp. 1117-1138, 2000.
22. [LL00] C. Lemieux and P. L'Ecuyer. 'A Comparison of Monte Carlo, Lattice Rules and Other Low-Discrepancy Point Sets', in Monte Carlo and Quasi-Monte Carlo methods 1998, (H. Niederreiter and J. Spanier Eds.), Springer, Berlin, pp. 326-340, 2000.
23. [NC06] D. Nuyens and R. Cools. 'Fast Component-By-Component Construction of Rank-1 Lattice Rules in Shift-Invariant Reproducing Kernel Hilbert Spaces' Math. Comp. 75, pp. 903-920, 2006.
24. [SA04] Z. Sandor and P. Andras. 'Alternative Sampling Methods for Estimating Multivariate Normal Probabilities', Journal of Econometrics, 120, pp. 207-234, 2004.
25. [Sc84] M. Schervish. 'Multivariate Normal Probabilities with Error Bound', Applied Statistics 33, pp. 81-87, 1984.
26. [Sl02] I. H. Sloan. 'QMC Integration -Beating Intractability by Weighting the Co-ordinate Directions' in Monte Carlo and Quasi-Monte Carlo Methods 2000 (K. T. Fang, F. J. Hickernell, and H. Niederreiter, eds.), Springer-Verlag, Berlin, pp. 103-123, 2002.
27. [SJ94] I. H. Sloan and S. Joe. Lattice Methods for Multiple Integration, Oxford University Press, Oxford, 1994.
28. [So97] P. N. Somerville. 'Multiple Testing and Simultaneous Confidence Intervals: Calculation of Constants' Comp. Stat. & Data Analysis 25, pp. 217-223, 1997.
29. [So98a] P. N. Somerville. 'Numerical Computation of Multivariate Normal and Multivariate-T Probabilities Over Convex Regions', J. Comput. Graph. Stat. 7, pp. 529-545, 1998.
30. [So98b] P. N. Somerville. 'A Fortran 90 Program for Evaluation of Multivariate Normal and Multivariate t Integral over Convex Regions', Journal of Statistical Software 3, 1998, available at http://www.jstatsoft.org.
31. [So99] P. N. Somerville. 'Critical Values for Multiple Testing and Comparisons: One Step and Step Down Procedures' J. Stat. Plan. & Inf., 82, pp. 129-138, 1999.
32. [So01] P. N. Somerville. 'Numerical Computation of Multivariate Normal and Multivariate t Probabilities over Ellipsoidal regions. Journal of Statistical Software 6, 2001, available at http://www.jstatsoft.org.
33. [St90] G. W. Stewart. 'The Efficient Generation of Random Orthogonal Matrices with An Application to Condition Estimation', SIAM J. Numer. Anal. 17, pp. 403-409, 1980.
34. [To90] Y. L. Tong. The Multivariate Normal Distribution, Springer-Verlag, New York, 1990.
35. [Vi96] W. P. M. Vijverberg. 'Monte Carlo Evaluation of Multivariate Student's t Probabilities', Economics Letters 52, pp. 1-6, 1996.
36. [Vi97] W. P. M. Vijverberg. 'Monte Carlo Evaluation of Multivariate Normal Probabilities',Journal of Econometrics 76, pp. 281-307, 1997.
37. [Vi00] W. P. M. Vijverberg. 'Rectangular and Wedge-shaped Multivariate Normal Probabilities', Economics Letters 68, pp. 13-20, 2000.