On Nonparametric Estimation of the Fisher Information

Wei Cao, Alex Dytso, Michael Faus, H. Vincent Poor, Gang Feng

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


This paper considers a problem of estimation of the Fisher information for location from a random sample of size n. First, an estimator proposed by Bhattacharya is revisited and improved convergence rates are derived. Second, a new estimator, termed clipped estimator, is proposed. The new estimator is shown to have superior rates of convergence as compared to the Bhattacharya estimator, albeit with different regularity conditions. Third, both of the estimators are evaluated for the practically relevant case of a random variable contaminated by Gaussian noise. Moreover, using Brown's identity, which relates the Fisher information to the minimum mean squared error (MMSE) in Gaussian noise, a consistent estimator for the MMSE is proposed.

Original languageEnglish (US)
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781728164328
StatePublished - Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: Jul 21 2020Jul 26 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


  • Fisher information
  • MMSE
  • Nonparametric estimation
  • kernel estimation


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