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Robust hierarchical Bayes estimation of exchangeable means
Author(s) -
Angers JeanFrançois,
Berger James O.
Publication year - 1991
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315535
Subject(s) - mathematics , estimator , bayes' theorem , cauchy distribution , statistics , bayes estimator , multivariate statistics , prior probability , multivariate normal distribution , bayesian probability
Estimation of the mean of a multivariate normal distribution is considered. The components of the mean vector θ are assumed to be exchangeable; this is modelled in a hierarchical fashion with independent Cauchy distributions as the first‐stage prior. The resulting generalized Bayes estimator is calculated and shown to be robust with respect to the presence of outlying means. Alternative estimators that have similar behaviour but are cheaper to compute are also derived.