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Cramer-Rao Bounds for Misspecified Models

Vuong, Quang H. (1986) Cramer-Rao Bounds for Misspecified Models. Social Science Working Paper, 652. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20170823-162930200

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Abstract

In this paper, we derive some lower bounds of the Cramer-Rao type for the covariance matrix of any unbiased estimator of the pseudo-true parameters in a parametric model that may be misspecified. We obtain some lower bounds when the true distribution belongs either to a parametric model that may differ from the specified parametric model or to the class of all distributions with respect to which the model is regular. As an illustration, we apply our results to the normal linear regression model. In particular, we extend the Gauss-Markov Theorem by showing that the OLS estimator has minimum variance in the entire class of unbiased estimators of the pseudo-true parameters when the mean and the distribution of the errors are both misspecified.


Item Type:Report or Paper (Discussion Paper)
Additional Information:This research was supported by National Science Foundation Grant SES-8410593. I am indebted to D. Rivers for helpful discussions. This paper is dedicated to those who have made this past year enjoyable. Remaining errors are mine.
Group:Social Science Working Papers
Funders:
Funding AgencyGrant Number
NSFSES-8410593
Series Name:Social Science Working Paper
Issue or Number:652
Record Number:CaltechAUTHORS:20170823-162930200
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170823-162930200
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80751
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:08 Sep 2017 21:55
Last Modified:03 Oct 2019 18:34

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