The expected missing mass under an entropy constraint

Daniel Berend, Aryeh Kontorovich, Gil Zagdanski

Research output: Contribution to journalArticlepeer-review

Abstract

In Berend and Kontorovich (2012), the following problem was studied: A random sample of size t is taken from a world (i.e., probability space) of size n; bound the expected value of the probability of the set of elements not appearing in the sample (unseen mass) in terms of t and n. Here we study the same problem, where the world may be countably infinite, and the probability measure on it is restricted to have an entropy of at most h. We provide tight bounds on the maximum of the expected unseen mass, along with a characterization of the measures attaining this maximum.

Original languageAmerican English
Article number315
Pages (from-to)1-13
JournalEntropy
Volume19
Issue number7
DOIs
StatePublished - 1 Jul 2017

Keywords

  • Entropy
  • Missing mass
  • Probability estimate
  • Sampling

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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