The Annals of Statistics

Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance

John J. Miller

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 5, Number 4 (1977), 746-762.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343897

Digital Object Identifier
doi:10.1214/aos/1176343897

Mathematical Reviews number (MathSciNet)
MR448661

Zentralblatt MATH identifier
0406.62017

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62J10: Analysis of variance and covariance

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

Citation

Miller, John J. Asymptotic Properties of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance. Ann. Statist. 5 (1977), no. 4, 746--762. doi:10.1214/aos/1176343897. https://projecteuclid.org/euclid.aos/1176343897


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