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A Bernstein-type inequality for suprema of random processes with applications to model selection in non-Gaussian regression
Let $(X_t)_{t∈T}$ 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 $Z = \sup_{t∈T} X_t$ by using the generic chaining device introduced in Talagrand (Inst. Hautes Études …