A Bernstein Inequality For Exponentially Growing Graphs

2017/01/16 by Krebs, Johannes T. N. · 1 citation
#62G08 #62M40 #90B15 #91D30 #FOS: Mathematics #Primary: 62G20 #Secondary: 62G07 #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1701.04188

Abstract

In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in highly-connected networks. It can be useful to obtain consistency properties for nonparametric estimators of conditional expectation functions which are derived from such networks.

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