Comment on the difficultie you may encounter if you want to study the Cramer–von Mises ´ statistic in the bivariate (or multivariate) case where the distribution function F(x) is define on   and is...

Comment on the difficultie you may encounter if you want to study the Cramer–von Mises ´ statistic in the bivariate (or multivariate) case where the distribution function F(x) is define on
  and is not necessarily expressible as the product of its marginal distributions.

Consider the Kolmogorov–Smirnov statistic for the one-sample and two-sample problems, and comment why you do not expect the asymptotic normality to be tenable in such cases. (See Chapter 11 for more details on their asymptotic distributions.)

Chapter 8