2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | E.3.1 | ||
| Paper Title | A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications | ||
| Authors | Alex Dytso, H. Vincent Poor, Shlomo Shamai (Shitz), Princeton University, United States | ||
| Session | E.3: Estimation Theory | ||
| Presentation | Lecture | ||
| Track | Detection and Estimation | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | This paper provides a general derivative identity for the conditional mean estimator of an arbitrary vector signal in Gaussian noise with an arbitrary covariance matrix. This new identity is used to recover and generalize many known identities in the literature and derive some new identities. For example, a new identity is discovered, which shows that an arbitrary higher-order conditional moment is completely determined by the first conditional moment. Several applications of the identities are shown. For instance, by using one of the identities, a simple proof of the uniqueness of the conditional mean estimator as a function of the distribution of the signal. Moreover, one of the identities is used to extend the notion of empirical Bayes to higher-order conditional moments. Specifically, based on a random sample of noisy observations, a consistent estimator for a conditional expectation of any order is derived. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
