Open Access
2013 On the concentration of the missing mass
Daniel Berend, Aryeh Kontorovich
Author Affiliations +
Electron. Commun. Probab. 18: 1-7 (2013). DOI: 10.1214/ECP.v18-2359


A random variable is sampled from a discrete distribution. The missing mass is the probability of the set of points not observed in the sample. We sharpen and simplify McAllester and Ortiz's results (JMLR, 2003) bounding the probability of large deviations of the missing mass. Along the way, we refine and rigorously prove a fundamental inequality of Kearns and Saul (UAI, 1998).


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Daniel Berend. Aryeh Kontorovich. "On the concentration of the missing mass." Electron. Commun. Probab. 18 1 - 7, 2013.


Accepted: 9 January 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60050
MathSciNet: MR3011530
Digital Object Identifier: 10.1214/ECP.v18-2359

Primary: 60F10
Secondary: 39B72

Keywords: Hoeffding inequality , measure concentration , missing mass

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