2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | S.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. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
