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July 1, 1977The Annals of StatisticsOpen Access

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

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Determine the asymptotic behavior, consistency, and efficiency of maximum likelihood estimators within mixed-model analysis of variance frameworks.
Applied generalized asymptotic theorems for maximum likelihood estimation developed by Weiss (1971, 1973) to mixed ANOVA models.
Accounted for non-identically distributed observations and varying normalizing sequences across different parameter dimensions.
Proved the existence of a sequence of likelihood equation roots that is consistent and asymptotically normally distributed.
Demonstrated estimator efficiency via attainment of the Cramér-Rao lower bound for the asymptotic covariance matrix.
Provided specific analytical examples and established theoretical properties for likelihood ratio tests in these mixed models.

Authors

JMJ. J. MillerStatistical and Applied Mathematical Sciences Institute

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Implication

Theoretical statistical analysis demonstrates consistency, asymptotic normality, and efficiency of maximum likelihood estimators in mixed ANOVA models, confirming optimal large-sample properties.

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J. J. Miller (1977) studied this question.

synapsesocial.com/papers/6a0f96ddb6f5ee04015fd2fd https://doi.org/10.1214/aos/1176343897

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Implication

Theoretical statistical analysis demonstrates consistency, asymptotic normality, and efficiency of maximum likelihood estimators in mixed ANOVA models, confirming optimal large-sample properties.

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

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

Key Points

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Implication

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