Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 3, 545--560

CREDIBLE AND CONFIDENCE SETS FOR THE RATIO OF VARIANCE COMPONENTS IN THE BALANCED ONE-WAY MODEL

By

TONGLIN ZHANG, Purdue University, USA
and
MICHAEL WOODROOFE, University of Michigan, USA

SUMMARY. Classical confidence intervals for the ratio of variance components can degenerate to a single point with positive probability, leaving no allowance for error. An alternative method is considered which avoids this problem, but maintains the frequentist coverage probability. The alternative intervals are compared to Bayesian credible intervals, derived from a non-informative prior; and the Bayesian intervals are shown to have quite high frequentist coverage probabilities.

AMS (1991) subject classification}. 62F15, 62J10, 62F25.

Key words and phrases. Between variance, frequentist coverage probability, prior and posterior distributions, total positivity, unimodality, within variance.

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