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Estimation of the common mean from heterogeneous normal observations with unknown variances
Author(s) -
Rukhin Andrew L.
Publication year - 2017
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12227
Subject(s) - statistics , mathematics , estimator , statistic , bayes' theorem , maximum likelihood , normal distribution , posterior probability , variance (accounting) , restricted maximum likelihood , bayesian probability , accounting , business
Summary To determine the common mean of heterogeneous normal observations, the Bayes procedures and the invariant maximum likelihood estimators of the weights forming the weighted means statistic are obtained when there are no variance estimates. The Bayes statistic is based on the reference, Geisser–Cornfield prior distribution which makes the posterior (discrete) distribution of the mean to be supported by the observed data with probabilities determined via the geometric means of the distances between data points. The maximum likelihood estimator coincides with the observation which has the maximal posterior probability. These procedures can be useful when measurement uncertainties are not reported or are misspecified.