Estimation of the common mean from heterogeneous normal observations with unknown variances

• 成果类型: Article
• 署名作者: Rukhin, Andrew L.
• 署名单位: National Institute of Standards & Technology (NIST) - USA
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12231
• 发表日期: 2017
• 页码: 1601-1618
• 关键词: fundamental physical constants; codata recommended values; metaanalysis

摘要

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.