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arXiv · 1809.02495

A note on concentration inequality for vector-valued martingales with weak exponential-type tails

Chris Junchi Li
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Abstract

We present novel martingale concentration inequalities for martingale differences with finite Orlicz-$ψ_α$ norms. Such martingale differences with weak exponential-type tails scatters in many statistical applications and can be heavier than sub-exponential distributions. In the case of one dimension, we prove in general that for a sequence of scalar-valued supermartingale difference, the tail bound depends solely on the sum of squared Orlicz-$ψ_α$ norms instead of the maximal Orlicz-$ψ_α$ norm, generalizing the results of Lesigne & Volný (2001) and Fan et al. (2012). In the multidimensional case, using a dimension reduction lemma proposed by Kallenberg & Sztencel (1991) we show that essentially the same concentration tail bound holds for vector-valued martingale difference sequences.

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Chris Junchi Li. 2020-03-18. A note on concentration inequality for vector-valued martingales with weak exponential-type tails. https://arxiv.org/abs/1809.02495

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