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2011

The Bernstein-Orlicz norm and deviation inequalities

van de Geer, Sara, Lederer, Johannes

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We introduce two new concepts designed for the study of empirical processes.

First, we introduce a new Orlicz norm which we call the Bernstein-Orlicz norm.
This new norm interpolates sub-Gaussian and sub-exponential tail behavior.
In particular, we show how this norm can be used to simplify the derivation of deviation inequalities for suprema of collections of random variables.

The Bernstein-Orlicz norm and deviation inequalities · Around

Built on

On the Convergence of Empiric Distribution Functions
J.R. Blum · 1955
Earlier work this paper cites.
Convex functions and Orlicz spaces
M.A. Krasnosel’skii and Y.B. Rutickii · 1961
Earlier work this paper cites.
Probability inequalities for sums of independent random variables
G. Bennet · 1962
Earlier work this paper cites.
The sizes of compact subsets of hilbert space and continuity of gaussian processes
R.M. Dudley · 1967
Earlier work this paper cites.
A central limit theorem under metric entropy with L 2 L_{2} bracketing
M. Ossiander · 1987
Earlier work this paper cites.

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