@inproceedings{5f18891f17224507918155a15caf037c,
title = "L1 Estimation in Gaussian Noise: On the Optimality of Linear Estimators",
abstract = "Consider the problem of estimating a random variable X in Gaussian noise under L1 fidelity criteria. It is well-known that in the L1 setting, the optimal Bayesian estimator is given by the conditional median. The goal of this work is to characterize the set of prior distributions on X for which the conditional median corresponds to a linear estimator. This work shows that neither discrete nor compactly supported distributions can induce a linear conditional median. Moreover, under certain non-trivial restrictions on the set of allowed probability distributions, the Gaussian is shown to be the only solution that induces a linear conditional median.",
author = "Barnes, {Leighton P.} and Alex Dytso and Poor, {H. Vincent}",
note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2023 IEEE International Symposium on Information Theory, ISIT 2023 ; Conference date: 25-06-2023 Through 30-06-2023",
year = "2023",
doi = "10.1109/ISIT54713.2023.10206980",
language = "English (US)",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1872--1877",
booktitle = "2023 IEEE International Symposium on Information Theory, ISIT 2023",
address = "United States",
}