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Bivariate symmetric statistics of
long-range dependent observations
Herold Dehling
Murad S. Taqqu
Abstract:
Let be a stationary,
mean-zero Gaussian sequence with covariances satisfying
and where D is small and L is slowly varying
at infinity. Consider the sequence ,
where G is any measurable
function. We obtain the asymptotic distribution of certain degenerate von
Mises and U-statistics based on the . As applications, we consider the
sample variance, the -squared goodness of fit test and the Cramer-von
Mises-Smirnov criterion. The results are non-standard.