A unified approach to Cramér-rao inequalities

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Abstract

A unified approach is presented for establishing a broad class of Cramér-Rao inequalities for the location parameter, including, as special cases, the original inequality of Cramér and Rao, as well as an L p version recently established by the authors. The new approach allows for generalized moments and Fisher information measures to be defined by convex functions that are not necessarily homogeneous. In particular, it is shown that associated with any log-concave random variable whose density satisfies certain boundary conditions is a Cramér-Rao inequality for which the given log-concave random variable is the extremal. Applications to specific instances are also provided.

Original languageEnglish (US)
Article number6655985
Pages (from-to)643-650
Number of pages8
JournalIEEE Transactions on Information Theory
Volume60
Issue number1
DOIs
StatePublished - Jan 2014

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Keywords

  • Cramér-Rao inequality
  • Fisher information
  • Rényi entropy
  • Shannon entropy
  • entropy
  • information measure
  • moment

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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