Small-sample inference about variance and its transformations
N.T. Longford
Abstract
We discuss minimum mean squared error and Bayesian estimation
of variances and of some of their common transformations
in the setting of normality and homoscedasticity with small samples,
for which asymptotics do not apply.
We show that permitting some bias can be rewarded
by greatly reduced mean squared error.
We draw inferences about the variance of a small normal random sample
by using borderline and equilibrium priors.
The purpose of these priors is to reduce the onus on the expert or client
to specify a single prior distribution
that would capture the information available prior to data inspection.
Instead, the (parametric) class of all priors considered is partitioned
to subsets that result in different optimal decisions.
The Bayesian approach can be formulated in the frequentist paradigm,
describing the prior as being equivalent to additional observations.
SORT, Journal of the Catalan Statistical Institute 34, 3-20, 2010.
June 2010.