ON SMOOTHNESS CONDITIONS AND CONVERGENCE-RATES IN THE CLT IN BANACH-SPACES
Bentkus, V
Bentkus
V
Götze, Friedrich
Götze
Friedrich
In Banach spaces the rate of convergence in the Central Limit Theorem is of order O(n-1/2) for sets which have 'regular' boundaries with respect to the given covariance structure and which are three times differentiable. We show that in infinite dimensional spaces it is impossible to weaken this differentiability condition in general, whereas in finite dimensional spaces the assumption of convexity suffices. Similar results hold for the expectation of smooth functionals.
96
2
137-151
137-151
SPRINGER VERLAG
1993