Technical Program

Paper Detail

Paper IDS.9.1
Paper Title On Nonparametric Estimation of the Fisher Information
Authors Wei Cao, University of Electronic Science and Technology of China, China; Alex Dytso, Michael Fauss, H. Vincent Poor, Princeton University, United States; Gang Feng, University of Electronic Science and Technology of China, China
Session S.9: Information Measures I
Presentation Lecture
Track Shannon Theory
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract 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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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