Under natural conditions on a class F of functions on a probability space, near optimal bounds are given for the probabilities P(f|∑i≤ n f(Xᵢ) - nE(f)| ≥ M√ n). The method is a variation of this author's method to study the tail probability of the supremum of a Gaussian process.
No takes yet. Share an insight, caveat, or question.
Michel Talagrand (1994) studied this question.