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July, 1977 Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance
John J. Miller
Ann. Statist. 5(4): 746-762 (July, 1977). DOI: 10.1214/aos/1176343897

Abstract

We show that in the mixed model of the analysis of variance, there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal, and efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix. These results follow directly by an application of a general result of Weiss (1971, 1973) concerning maximum likelihood estimates. This problem differs from standard problems in that we do not have independent, identically distributed observations and that estimates of different parameters may require normalizing sequences of different orders of magnitude. We give some examples and comment briefly on likelihood ratio tests for these models.

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John J. Miller. "Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance." Ann. Statist. 5 (4) 746 - 762, July, 1977. https://doi.org/10.1214/aos/1176343897

Information

Published: July, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0406.62017
MathSciNet: MR448661
Digital Object Identifier: 10.1214/aos/1176343897

Subjects:
Primary: 62E20
Secondary: 62J10

Keywords: Analysis of variance , asymptotic normality , consistency , maximum likelihood estimates , mixed model

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 4 • July, 1977
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