- Beckers, M. and Haegemans, A. (1992)
`Comparison of Numerical Integration Techniques for Multivariate Normal
Integrals', Computer Science Department preprint,
Catholic University of Leuven, Belgium.
- Berntsen, J., Espelid, T. O. and Genz, A. (1991)
`Algorithm 698: DCUHRE-An Adaptive Multidimensional Integration
Routine for a Vector of Integrals',
ACM Transactions on Mathematical Software 17, pp. 452-456.
- Cornish, E. A. (1954)
`The Multivariate t-Distribution Associated with a Set of Normal Sample
Deviates'
Australian Journal of Physics 7, pp. 531-542.
- Cranley, R. and Patterson, T. N. L. (1976)
`Randomization of Number Theoretic Methods for Multiple Integration',
SIAM J. Numer. Anal. 13, pp. 904-914.
- Davis, P. J. and Rabinowitz P. (1984),
Methods of Numerical Integration,
Academic Press, New York.
- Deák, I. (1980)
`Three Digit Accurate Multiple Normal Probabilities'
Numer. Math. 35, pp. 369-380.
- Deák, I. (1986)
`Computing Probabilities of Rectangles in Case of
Multinormal Distribution'
J. Statist. Comput. Simul. 26, pp. 101-114.
- Deák, I. (1990)
Random Number Generation and Simulation,
Akadémiai Kiadó, Budapest, Chapter 7.
- Fang, K.-T., and Wang, Y. (1994)
Number-Theoretic Methods in Statistics,
Chapman and Hall, London, pp. 167-170.
- Genz, A. (1992)
`Numerical Computation of the Multivariate Normal Probabilities',
J. Comput. Graph. Stat. 1, pp. 141-150.
- Genz, A. (1993),
'A Comparison of Methods for Numerical Computation of
Multivariate Normal Probabilities',
Computing Science and Statistics 25, pp. 400-405.
- Genz, A. and Kwong, K. S. (1999)
`Numerical Evaluation of Singular Multivariate Normal Distributions',
submitted.
- Genz, A. and Bretz, F. (1999)
`Numerical Computation of the Multivariate t Probabilities with Application
to Power Calculation of Multiple Contrasts',
Journal of Statistical Computation and Simulation 63, pp. 361-378.
- Gibson, G. J., Glasbey, C. A. and Elston, D. A. (1992)
`Monte-Carlo Evaluation of Multivariate Normal Integrals',
Scottish Agricultural Statistics Service preprint,
University of Edinburgh, Scotland.
- Hajivassiliou, V., McFadden, D. and Rudd, O. (1996).
`Simulation of Multivariate Normal Rectangle Probabilities and Their
Derivatives: Theoretical and Computational Results',
Journal of Econometrics, 72, pp. 85-134.
- Hickernell, F. J. (1998).
`A Generalized Discrepancy and Quadrature Error Bound',
Mathematics of Computation, 67, pp. 299-322.
- Hsu, Jason C. (1996).
Multiple Comparisons, Chapman and Hall, London.
- Joe, S. (1995).
`Approximations to Multivariate Normal Rectangle Probabilities Based on
Conditional Expectations',
Journal of the American Statistical Association, 90, pp. 957-964.
- Johnson, Mark E. (1987).
Multivariate Statistical Simulation, Wiley, New York.
- Keast, P. (1973)
`Optimal Parameters for Multidimensional Integration',
SIAM J. Numer. Anal. 10, pp. 831-838.
- Lepage, G. Peter (1978)
`A New Algorithm for Adaptive Multidimensional Integration',
J. Computational Physics 27, pp. 192-203.
- Lohr, S. (1990)
`Accurate Multivariate Estimation using Triple Sampling',
Ann. Statist. 18, pp. 1615-1633.
- Marsaglia, G. and Olkin, I. (1984)
`Generating Correlation Matrices',
SIAM Journal of Scientific and Statistical Computing
5, pp. 470-475.
- Schervish, M. (1984)
`Multivariate Normal Probabilities with Error Bound',
Applied Statistics 33, pp. 81-87.
- Sloan, I. H., and Joe, S. (1994)
Lattice Methods for Multiple Integration,
Oxford University Press, Oxford.
- Somerville, P. N. (1997)
`Multiple Testing and Simultaneous Confidence Intervals: Calculation of
Constants'
Comp. Stat. & Data Analysis 25, pp. 217-223.
- Somerville, P. N. (1998))
`Numerical Computation of Multivariate Normal and Multivariate-t
Probabilities Over Convex Regions',
J. Comput. Graph. Stat. 7, pp. 529-545.
- Somerville, P. N. (1999)
`Critical Values for Multiple Testing and Comparisons: One Step and
Step Down Procedures'
J. Stat. Plan. & Inf. 82, pp. 129-138.
- Stewart, G. W. (1980),
'The Efficient Generation of Random Orthogonal Matrices with
An Application to Condition Estimation',
SIAM J. Numer. Anal. 17, 403-409.
- Tong, Y. L. (1990)
The Multivariate Normal Distribution,
Springer-Verlag, New York.
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