Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts

Journal of Statistical Computation and Simulation

Volumn 63, Issue 4, 1999, Pages 103-117

  Genz, Alan ^a   Bretz, Frank ^b  

^a WASHINGTON STATE UNIVERSITY   (United States)

^b LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Calculation of power; Lattice rule algorithm; Monte Carlo methods; Multiple contrast test; Multivariate t distribution

Indexed keywords

EID: 0033243578     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659908811962     Document Type: Article

References (34)

1. Bauer, P. (1997) A note on multiple testing procedures in dose finding. Biometrics, 53, 1125-1128.
2. Bretz, F. and Hothorn, L. (1999) A powerful alternative to Williams test with application to toxicological dose-response relationships of normally distributed data. Environmental and Ecological Statistics (under review).
3. Bristol, D. R. (1989) Designing clinical trials for two-sided multiple comparisons with a control. Controlled Clinical Trials, 10, 142-152.
4. Cornish, E. A. (1954) The multivariate t-distribution associated with a set of normal sample deviates. Australian Journal of Physics, 7, 531-542.
5. Deak, I. (1990) Random number generators and simulation. Akademiai Kiado, Budapest.
6. Dunn, O. J. and Massey, F. J. (1965) Estimation of multiple contrasts using t-distributions. Journal of the American Statistical Association, 60, 573-583.
7. Dunnett, C. W. (1955) A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50, 1096-1121.
8. Edwards, D. and Berry, J. (1987) The efficiency of simulation-based multiple comparisons. Biometrics, 43, 913-928.
9. Genz, A. (1992) Numerical computation of the multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1, 141-150.
10. Genz, A. (1993) Numerical computation of the multivariate t-probabilities. Talk held on SIAM Simulation and MC Methods, San Francisco.
11. Hajivassiliou, V., McFadden, D. and Ruud, P. (1996) Simulation of multivariate normal rectangle probabilities and their derivatives: Theoretical and computational results. Journal of Econometrics, 72, 85-134.
12. Hayter, A. J. and Liu, W. (1992) A method of power assessment for tests comparing several treatments with a control. Communications in Statistics - Theory and Methods, 21, 1871-1889.
13. Hochberg, Y. and Tamhane, A. (1987) Multiple comparison procedures. Wiley, New York.
14. Hothorn, L. A., Neuhäuser, M. and Koch, H. F. (1997) Analysis of randomised dose-finding studies: closure test modifications based on multiple contrast tests. Biometrical Journal, 39, 467-479.
15. Hsu, J. C. (1992) The factor analytic approach to simultaneous inference in the general linear model. Journal of Computational and Graphical Statistics, 1, 151-168.
16. Hsu, J. C. and Nelson, B. L. (1990) Control variates for quantile estimation. Management Science, 36, 835-951.
17. Hsu, J. C. and Nelson, B. L. (1998) Multiple comparisons in the general linear model. Journal of Computational and Graphical Statistics, 7, 23-41.
18. Joe, H. (1995) Approximations to multivariate normal rectangle probabilities based on conditional expectations. Journal of the American Statistical Association, 90, 957-64.
19. Joe, S. (1990) Randomization of lattice rules for numerical multiple integration. Journal of Computational and Applied Mathematics, 31, 299-304.
20. Korobov, N. M. (1960) Properties and calculation of optimal coefficients. Soviet Math. Doklady, 1, 696-700.
21. Mukerjee, H., Robertson, T. and Wright, F. T. (1986) Multiple contrast tests for testing against a simple tree ordering. In: Advances in Order Restricted Statistical Inference, Dykstra, R. (Ed.), Springer, Berlin, pp. 203-230.
22. Mukerjee, H., Robertson, T. and Wright, F. T. (1987) Comparison of several treatments with a control using multiple contrasts. Journal of the American Statistical Association, 82, 902-910.
23. Niederreiter, H. (1992) Random number generation and quasi-Monte Carlo methods. Society for Industrial and Applied Mathematics, Philadelphia.
24. Ralston, A. and Rabinowitz, P. (1978) A first course in numerical analysis. McGraw-Hill, New York.
25. Schervish, M. J. (1984) Algorithm AS 195: multivariate normal probabilities with error bound. Applied Statistics, 33, 81-94. Correction: (1985), 34, 103-104.
26. Schervish, M. J. (1984) Algorithm AS 195: multivariate normal probabilities with error bound. Applied Statistics, 33, 81-94. Correction: (1985), 34, 103-104.
27. Sloan, I. H. and Joe, S. (1994) Lattice methods for multiple integration. Clarendon Press, Oxford.
28. Solow, A. R. (1990) A method for approximating multivariate normal orthant probabilities. Journal of Statistical Computation and Simulation, 37, 225-229.
29. Somerville, P. (1997) Multiple testing and simultaneous confidence intervals: calculation of constants. Computational Statistics and Data Analysis, 25, 217-233.
30. Somerville, P. (1998) Numerical computation of multivariate normal and multivariate t-probabilities. Journal of Computational and Graphical Statistics, 7, 529-544.
31. Tamhane, A. C., Dunnett, C. W. and Hochberg, Y. (1996) Multiple test procedures for dose finding. Biometrics, 52, 21-37.
32. Wang, O. and Kennedy, W. J. (1997) Application of numerical interval analysis to contain self-validating results for multivariate probabilities in a massively parallel environment. Statistics and Computing, 7, 163-171.
33. Westfall, P. H. (1997) Multiple testing of general contrasts using logical constraints and correlations. Journal of the American Statistical Association, 92, 299-306.
34. Williams, D. A. (1971) A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics, 27, 103-117.