Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 2, pp. 198-213

BAYESIAN ESTIMATION OF INTRA-BLOCK EXCHANGEABLE NORMAL MEANS WITH APPLICATIONS

By

JEAN-FRANÇOIS ANGERS , Université de Montréal, Montréal
BRENDA MACGIBBON, Université du Québec à Montréal, Montréal
SHUPEI WANG, Hôpital Ste-Justine, Montréal

SUMMARY. Estimation of the mean of a multivariate normal distribution is considered. The components of the mean vector are assumed to be intra-block exchangeable; this is modelled in a hierarchical Bayesian fashion with a multivariate normal distribution as the first stage prior. The resulting Bayes estimator is calculated and shown to be robust with respect to the presence of outlying coordinates in the vector of observations. The use of the proposed estimator is illustrated on data sets from an animal breeding experiment and from a clinical trial.

AMS (1991) subject classification.Primary 62F35.; secondary 62E25.

Key words and phrases. Robust estimator, Bayes estimator, hierarchical Bayes model, admissibility, mixed-linear models, outlier.

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