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\noindent Statistica Sinica {\bf 13}(2003), 327-349
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\centerline{\large\bf THE LIMIT DISTRIBUTION OF A TEST STATISTIC}
\vspace{2pt}
\centerline{\large\bf FOR BIVARIATE NORMALITY}
\vspace{.25cm}
\centerline{Namhyun Kim and Peter J. Bickel}
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\centerline{\it Hongik University and University of California, Berkeley}
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\begin{quotation}
\noindent {\it 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. \par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Bivariate normality, Brownian bridge, Gaussian process.
\end{quotation}
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