On Hoeffding’s Inequality for Dependent Random Variables

Sara A. van de Geer ()
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Sara A. van de Geer: University of Leiden, Mathematical Institute

A chapter in Empirical Process Techniques for Dependent Data, 2002, pp 161-169 from Springer

Abstract: Abstract Let {Z θ : θ ∈ Θ} be a random process indexed by a parameter θ in some (metric) space Θ. Given an appropriate moment or probability inequality for each fixed θ (a pointwise inequality), one can often derive an inequality that holds uniformly in θ ∈ Θ by applying the chaining technique. Therefore, pointwise inequalities are (apart from being of intrinsic interest) quite relevant within the theory of stochastic processes. We present a generalization of Ho-effding’s inequality, and the related bounded difference inequality of McDiarmid [7]. We also state the corresponding uniform inequality. As an application, we consider estimation in the autoregression model.

Keywords: Empirical Process; Important Special Case; Orlicz Function; Dependent Random Variable; Probability Inequality (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0099-4_4

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DOI: 10.1007/978-1-4612-0099-4_4

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