Discrepancy, chaining and subgaussian processes
نویسندگان
چکیده
منابع مشابه
Discrepancy, Chaining and Subgaussian Processes
We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf(εi) supf∈F | ∑k i=1 εif(Xi)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of R using properties of ...
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It can be checked that this is a valid norm (on the set of random variables for which the left side of the above display is finite). Of special interest to us will be the Orlicz norms corresponding to the functions {ψp : p ≥ 1} where ψp(x) = exp(xp) − 1. Lemma 8.1 of Kosorok (2008) provides a necessary and sufficient condition for the ψp Orlicz norm to be finite in terms of the tail-behavior of...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2011
ISSN: 0091-1798
DOI: 10.1214/10-aop575