Conclusions

The present paper compared several methods for approximating multivariate $t$ probabilities. The methods can be classified into inequality based methods which provide either an upper or a lower bound of the true integral value and other approximations, which mostly rely on replacing the true correlation matrix through a more convenient matrix. The numerical comparisons show that the true critical values are approximated with satisfactory accuracy for practical purposes. The modification described in this paper of the hybrid bounds by Tomescu (1986) are quickly implemented and run at low computation time. These hybrid bounds usually yielded three digit accurate values for the typical multiple comparison problems which we looked at. All results are also valid for multivariate normal problems.

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