A Bernstein inequality for exponentially growing graphs. Issue 20 (18th October 2018)

• Record Type: Journal Article
• Authors: Krebs, Johannes T. N.
• Is Part Of: Communications in statistics. Volume 47:Issue 20(2018)
• Page Start: 5097
• Page End: 5106
• Publication Date: 2018-10-18
• Subjects: Asymptotic inference -- asymptotic inequalities -- Bernstein inequality -- concentration inequality -- graphs -- highly connected graphical networks -- mixing -- non parametric statistics -- random fields -- stochastic processes; Primary: 62G20, 62M40, 90B15 -- Secondary: 62G07, 62G08, 91D30; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1386317
• Languages: English
• ISSNs: 0361-0926

Abstract

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