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

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

doi:10.1109/ISIT54713.2023.10206620

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 proceeding › Conference contribution › peer-review

2 Scopus citations

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 language	English
Title of host publication	2023 IEEE International Symposium on Information Theory, ISIT 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2655-2660
Number of pages	6
ISBN (Electronic)	9781665475549
DOIs	https://doi.org/10.1109/ISIT54713.2023.10206620
State	Published - 2023
Externally published	Yes
Event	2023 IEEE International Symposium on Information Theory, ISIT 2023 - Taipei, Taiwan, Province of China Duration: 25 Jun 2023 → 30 Jun 2023

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2023-June
ISSN (Print)	2157-8095

Conference

Conference	2023 IEEE International Symposium on Information Theory, ISIT 2023
Country/Territory	Taiwan, Province of China
City	Taipei
Period	25/06/23 → 30/06/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

Parameter estimation
chi-square divergence
model mismatch
performance bounds

Access to Document

10.1109/ISIT54713.2023.10206620

Cite this

Weiss, A., Lancho, A., Bu, Y., & Wornell, G. W. (2023). A Bilateral Bound on the Mean-Square Error for Estimation in Model Mismatch. In 2023 IEEE International Symposium on Information Theory, ISIT 2023 (pp. 2655-2660). (IEEE International Symposium on Information Theory - Proceedings; Vol. 2023-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT54713.2023.10206620

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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.",

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Weiss, A, Lancho, A, Bu, Y & Wornell, GW 2023, A Bilateral Bound on the Mean-Square Error for Estimation in Model Mismatch. in 2023 IEEE International Symposium on Information Theory, ISIT 2023. IEEE International Symposium on Information Theory - Proceedings, vol. 2023-June, Institute of Electrical and Electronics Engineers Inc., pp. 2655-2660, 2023 IEEE International Symposium on Information Theory, ISIT 2023, Taipei, Taiwan, Province of China, 25/06/23. https://doi.org/10.1109/ISIT54713.2023.10206620

A Bilateral Bound on the Mean-Square Error for Estimation in Model Mismatch. / Weiss, Amir; Lancho, Alejandro; Bu, Yuheng et al.
2023 IEEE International Symposium on Information Theory, ISIT 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 2655-2660 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2023-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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

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