Estimating entropy on m bins given fewer than m samples

  • Authors:
  • L. Paninski

  • Affiliations:
  • Univ. Coll. London, UK

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

Consider a sequence pN of discrete probability measures, supported on mN points, and assume that we observe N independent and identically distributed (i.i.d.) samples from each pN. We demonstrate the existence of an estimator of the entropy, H(pN), which is consistent even if the ratio N/mN is bounded (and, as a corollary, even if this ratio tends to zero, albeit at a sufficiently slow rate).