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

Fingerprint

Cramer-Rao bounds
Model Misspecification
estimators
Parameter estimation
Parameter Estimation
Cramér-Rao Bound
Estimator
Common Mean
Specifications
Score Function
Model Specification
Misspecification
Unbiased estimator
Tie
specifications
Sharing
Necessary Conditions
requirements
Necessary
Model misspecification

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

On Constraints in Parameter Estimation and Model Misspecification. / Richmond, Christ.

2018 21st International Conference on Information Fusion, FUSION 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1080-1085 8455295.

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

Richmond, C 2018, On Constraints in Parameter Estimation and Model Misspecification. in 2018 21st International Conference on Information Fusion, FUSION 2018., 8455295, Institute of Electrical and Electronics Engineers Inc., pp. 1080-1085, 21st International Conference on Information Fusion, FUSION 2018, Cambridge, United Kingdom, 7/10/18. https://doi.org/10.23919/ICIF.2018.8455295
Richmond C. On Constraints in Parameter Estimation and Model Misspecification. In 2018 21st International Conference on Information Fusion, FUSION 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1080-1085. 8455295 https://doi.org/10.23919/ICIF.2018.8455295
Richmond, Christ. / On Constraints in Parameter Estimation and Model Misspecification. 2018 21st International Conference on Information Fusion, FUSION 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1080-1085
@inproceedings{c2a1895069694073b1a9c254d690cc7a,
title = "On Constraints in Parameter Estimation and Model Misspecification",
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.",
author = "Christ Richmond",
year = "2018",
month = "9",
day = "5",
doi = "10.23919/ICIF.2018.8455295",
language = "English (US)",
isbn = "9780996452762",
pages = "1080--1085",
booktitle = "2018 21st International Conference on Information Fusion, FUSION 2018",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - On Constraints in Parameter Estimation and Model Misspecification

AU - Richmond, Christ

PY - 2018/9/5

Y1 - 2018/9/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85054059391&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054059391&partnerID=8YFLogxK

U2 - 10.23919/ICIF.2018.8455295

DO - 10.23919/ICIF.2018.8455295

M3 - Conference contribution

SN - 9780996452762

SP - 1080

EP - 1085

BT - 2018 21st International Conference on Information Fusion, FUSION 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -