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Article Dans Une Revue Mathematical Methods of Statistics Année : 2013

Upper functions for positive random functionals. I. General setting and Gaussian random functions

Résumé

In this paper we are interested in finding upper functions for a collection real-valued random variables Ψ χ θ , θ ∈ Θ. Here {χ θ , θ ∈ Θ} is a family of continuous random mappings, Ψ is a given sub-additive positive functional and Θ is a totally bounded subset of a metric space. We seek a non-random function U : Θ → R+ such that sup θ∈Θ Ψ χ θ −U (θ) + is " small " with prescribed probability. We apply the results obtained in the general setting to the variety of problems related to gaussian random functions and empirical processes.
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Dates et versions

hal-01265252 , version 1 (31-01-2016)

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Oleg Lepski. Upper functions for positive random functionals. I. General setting and Gaussian random functions. Mathematical Methods of Statistics, 2013, 22 (1), pp.1-27. ⟨10.3103/S1066530713010018⟩. ⟨hal-01265252⟩
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