Anderson, T. W. and Sawa, Takamitsu (1980) Exact and Approximate Distributions of the Maximum Likelihood Estimator of a Slope Coefficient: The LIML Estimator for a Known Covariance Matrix. Social Science Working Paper, 326. California Institute of Technology , Pasadena, CA. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20171010-150811357
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Abstract
When the errors are normally independently distributed with equal variance, the maximum likelihood estimator of the slope of a linear functional relationship is the slope of the line minimizing the sum of squared deviations orthogonal to the line. The exact density and distribution of this estimator are obtained. Approximate distributions are obtained, and their accuracies are discussed.
| Item Type: | Report or Paper (Working Paper) | ||||||||||
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| Additional Information: | This work was supported in part by National Science Foundation Grant SOC77-14944 and SES79-13976 at the Institute for Mathematical Studies in the Social Sciences, Stanford University, and in part by NSF Grant SOC76-22232. The first author was a Sherman Fairchild Distinguished Scholar at the California Institute of Technology when this paper was completed. The authors are indebted to Naoto Kunitomo, Kimio Morimune, and Kanemi Ban for assistance in this research. Published as Anderson, T. W., and Takamitsu Sawa. "Exact and approximate distributions of the maximum likelihood estimator of a slope coefficient." Journal of the Royal Statistical Society. Series B (Methodological) (1982): 52-62. | ||||||||||
| Group: | Social Science Working Papers | ||||||||||
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| Subject Keywords: | Estimators, Maximum likelihood estimation, Maximum likelihood estimators, Covariance matrices, Approximation, Density estimation, Mathematical vectors, Coefficients, Technical reports, Fall lines | ||||||||||
| Series Name: | Social Science Working Paper | ||||||||||
| Issue or Number: | 326 | ||||||||||
| Record Number: | CaltechAUTHORS:20171010-150811357 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171010-150811357 | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 82265 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | Jacquelyn Bussone | ||||||||||
| Deposited On: | 11 Oct 2017 18:28 | ||||||||||
| Last Modified: | 03 Oct 2019 18:52 |
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