A Bernstein-type Inequality for Suprema of Random Processes with Applications to Model Selection in Non-gaussian Regression


Let (Xt)t∈T be a family of real-valued centered random variables indexed by a countable set T . In the first part of this paper, we establish exponential bounds for the deviation probabilities of the supremum Z = supt∈T Xt by using the generic chaining device introduced in Talagrand (1995). Compared to concentration-type inequalities, these bounds offer the… (More)