A Bilateral Bound on the Mean-Square Error for Estimation in Model Mismatch

Amir Weiss, Alejandro Lancho, Yuheng Bu, Gregory W. Wornell

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A bilateral (i.e., upper and lower) bound on the mean-square error under a general model mismatch is developed. The bound, which is derived from the variational representation of the chi-square divergence, is applicable in the Bayesian and nonBayesian frameworks to biased and unbiased estimators. Unlike other classical MSE bounds that depend only on the model, our bound is also estimator-dependent. Thus, it is applicable as a tool for characterizing the MSE of a specific estimator. The proposed bounding technique has a variety of applications, one of which is a tool for proving the consistency of estimators for a class of models. Furthermore, it provides insight as to why certain estimators work well under general model mismatch conditions.

Original languageEnglish
Title of host publication2023 IEEE International Symposium on Information Theory, ISIT 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2655-2660
Number of pages6
ISBN (Electronic)9781665475549
DOIs
StatePublished - 2023
Externally publishedYes
Event2023 IEEE International Symposium on Information Theory, ISIT 2023 - Taipei, Taiwan, Province of China
Duration: 25 Jun 202330 Jun 2023

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2023-June

Conference

Conference2023 IEEE International Symposium on Information Theory, ISIT 2023
Country/TerritoryTaiwan, Province of China
CityTaipei
Period25/06/2330/06/23

Keywords

  • chi-square divergence
  • model mismatch
  • Parameter estimation
  • performance bounds

All Science Journal Classification (ASJC) codes

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

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