On Constraints in Parameter Estimation and Model Misspecification

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Under perfect model specification several deterministic (non-Bayesian) parameter bounds have been established, including the Cramer-Rae, Bhattacharyya, and the Barankin bound; where each is known to apply only to estimators sharing the same mean as a function of the true parameter. This requirement of common mean represents a constraint on the class of estimators. While consideration of model misspecification is an additional complexity, the need for constraints remains a necessary consequence of applying the covariance inequality. These inherent constraints will be examined more closely under misspecification and discussed in detail along with a review of Vuong's original contribution of the misspecified Cramer-Rao bound (MCRB). Recent work derives the same MCRB as Vuong via a different approach, but applicable only to a class of estimators that is more restrictive. An argument is presented herein, however, that broadens this class to include all unbiased estimators of the pseudo-true parameters and strengthens the tie to Vuong's work. Interestingly, an inherent constraint of the covariance inequality, when satisfied by the choice in score function, yields a generalization of the necessary conditions identified by Blyth and Roberts to obtain an inequality of the Cramer-Rae type.

Original languageEnglish (US)
Title of host publication2018 21st International Conference on Information Fusion, FUSION 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1080-1085
Number of pages6
ISBN (Print)9780996452762
DOIs
StatePublished - Sep 5 2018
Event21st International Conference on Information Fusion, FUSION 2018 - Cambridge, United Kingdom
Duration: Jul 10 2018Jul 13 2018

Other

Other21st International Conference on Information Fusion, FUSION 2018
CountryUnited Kingdom
CityCambridge
Period7/10/187/13/18

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ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Signal Processing
  • Statistics, Probability and Uncertainty
  • Instrumentation

Cite this

Richmond, C. (2018). On Constraints in Parameter Estimation and Model Misspecification. In 2018 21st International Conference on Information Fusion, FUSION 2018 (pp. 1080-1085). [8455295] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ICIF.2018.8455295