A Bernstein-type inequality for suprema of random processes with an application to statistics

Yannick Baraud

Published 2009-04-21Version 1

We use the generic chaining device proposed by Talagrand to establish exponential bounds on the deviation probability of some suprema of random processes. Then, given a random vector $\xi$ in $\R^{n}$ the components of which are independent and admit a suitable exponential moment, we deduce a deviation inequality for the squared Euclidean norm of the projection of $\xi$ onto a linear subspace of $\R^{n}$. Finally, we provide an application of such an inequality to statistics, performing model selection in the regression setting when the errors are possibly non-Gaussian and the collection of models possibly large.