Cramer-Rao Bounds for Misspecified Models
- Creators
- Vuong, Quang H.
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.
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.Attached Files
Submitted - sswp652.pdf
Files
Name | Size | Download all |
---|---|---|
md5:1380770174832cc877d865604c2caba5
|
1.3 MB | Preview Download |
Additional details
- Eprint ID
- 80751
- Resolver ID
- CaltechAUTHORS:20170823-162930200
- SES-8410593
- NSF
- Created
-
2017-09-08Created from EPrint's datestamp field
- Updated
-
2019-10-03Created from EPrint's last_modified field
- Caltech groups
- Social Science Working Papers
- Series Name
- Social Science Working Paper
- Series Volume or Issue Number
- 652