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On the Robustness of Bayes Estimators of the Variance Ratio in Balanced One-Way ANOVA Models with Covariates

In: Statistical Theory and Applications

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  • Malay Ghosh
  • Robert M. Baskin

Abstract

This paper introduces some hierarchical Bayes (HB) estimators of the variance ratio in balanced one-way ANOVA models with covariates. Such estimators enjoy frequentist properties like consistency and asymptotic normality. Jackknifed estimators of the asymptotic variance of the HB estimators are found, and are used in the construction of asymptotic confidence intervals for the variance ratio. These intervals have larger coverage probability than similar intervals based on the maximum likelihood estimators, restricted maximum likelihood estimators, and estimators based on the Henderson-III method. The HB intervals are also much more robust than the competing intervals when the underlying distributions are double exponential or uniform.

Suggested Citation

  • Malay Ghosh & Robert M. Baskin, 1996. "On the Robustness of Bayes Estimators of the Variance Ratio in Balanced One-Way ANOVA Models with Covariates," Springer Books, in: H. N. Nagaraja & Pranab Kumar Sen & Donald F. Morrison (ed.), Statistical Theory and Applications, chapter 18, pages 217-231, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3990-1_18
    DOI: 10.1007/978-1-4612-3990-1_18
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