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Efficiency of Weighted Averages by W.J. Hall is a Mathematics article available to read on EtoBox.

What is Efficiency of Weighted Averages about?

When combining estimates of a common parameter (of dimension d 1) from independent data sets-as in stratified analyses and meta analyses-a weighted average, with weights 'proportional' to inverse variance matrices, is shown to have a minimal variance matrix (a standard fact when d = 1)-minimal in the sense that all convex combinations of the coordinates of the combined estimate have minimal variances. Minimum variance for the estimation of a single coordinate of the parameter can therefore be achieved by joint estimation of all coordinates using matrix weights. Moreover, if each estimate is asymptotically efficient within its own data set, then this optimally weighted average, with consistently estimated weights, is shown to be asymptotically efficient in the combined data set and avoids the need to merge the data sets and estimate the parameter in question afresh. This is so whatever additional non-common nuisance parameters may be in the models for the various data sets. A special case of this appeared in Fisher [1925. Theory of statistical estimation. Proc. Cambridge Philos. Soc. 22, 700-725.]: Optimal weights are 'proportional' to information matrices, and he argued that sample

Who reads Efficiency of Weighted Averages?

Author

W.J. Hall

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0378-3758)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)