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Lower bounds on the approximation of the multivariate empirical process. (English) Zbl 0554.60037
It is well-known that if C is the class of rectangles $$0\leq x_ 1\leq a_ 1$$, $$0\leq x_ 2\leq a_ 2$$ or the class of circular discs then the normalized empirical measure on C behaves like a Brownian bridge. Our main result shows that for these two classes the distances between the normalized empirical measure and the nearest Brownian measure have entirely different order of magnitudes.

MSC:
 60F15 Strong limit theorems 60J65 Brownian motion
Keywords:
empirical measure; Brownian bridge
Full Text:
References:
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