#### Estimation of Quadratic Functions: Noninformative Priors for
Non-Centrality Parameters

James O. Berger, Anne Philippe, and Christian P. Robert

The estimation of quadratic functions of a multivariate normal mean is
an inferential problem which, while being simple to state and often
encountered in practice, leads to surprising complications both from
frequentist and Bayesian points of view. The drawbacks of Bayesian inference
using the constant noninformative prior are now well established and we
consider in this paper the advantages and the shortcomings of alternative
noninformative priors. We take into account frequentist coverage probability
of confidence sets arising from these priors. Lastly, we derive some
optimality properties of the associated Bayes estimators in the special case of
independent components under quadratic loss.
Postscript File (686kB)