Abstract: Testing for normality has always been an important part of statistical methodology. In this paper we propose a test statistic for bivariate normality. We generalize the statistic proposed by de Wet and Venter to test bivariate normality using Roy's union-intersection principle. The generalized statistic is affine invariant. We show that the limit distribution of an approximation to the suggested statistic is representable as the supremum over an index set of the integral of a suitable Gaussian process. We also simulate the null distribution of the statistic, give some critical values of the distribution and make power comparisons to other procedures that have been proposed.
Key words and phrases: Bivariate normality, Brownian bridge, Gaussian process.