On the Rate of Clustering to the Strassen Set for Increments of the Uniform Empirical Process

摘要: We obtain outer rates of clustering in the functional laws iterated logarithm Deheuvels and Mason(11) Deheuvels,(7) which describe local oscillations empirical processes. Considering increment sizes an ↓ 0 such that nan ↑ ∞ nan(log n)−7/3 → we show sets properly rescaled functions cluster with probability one to en-enlarged Strassen ball B(0, 1) endowed uniform topology, where en may be chosen so small as e(log (1/an) + log n)−2/3 for any sufficiently large e. This speed coverage is reduced smaller an.