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A Bernstein inequality for exponentially growing graphs

: Krebs, J.


Communications in statistics. Theory and methods 47 (2018), No.20, pp.5097-5106
ISSN: 0361-0926 (Print)
ISSN: 1532-415X (Online)
Journal Article
Fraunhofer ITWM ()
asymptotic inference; asymptotic inequality; Bernstein inequality; concentration inequality; graph; highly connected graphical network; mixing; non parametric statistic; random field; stochastic process

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 non parametric estimators of conditional expectation functions which are derived from such networks.