Review Articles

Combining estimators of a common parameter across samples

Eric Slud ,

Mathematics Department, University of Maryland College Park, College Park, MD, USA; Center for Statistical Research and Methodology, US Census Bureau, Washington DC, USA

Ilia Vonta ,

Dept. of Mathematics, National Technical University of Athens, Athens, Greece

Abram Kagan

Mathematics Department, University of Maryland College Park, College Park, MD, USA

Pages 158-171 | Received 21 Mar. 2018, Accepted 28 Sep. 2018, Published online: 24 Oct. 2018,
  • Abstract
  • Full Article
  • References
  • Citations


In many settings, multiple data collections and analyses on the same topic are summarised separately through statistical estimators of parameters and variances, and yet there are scientific reasons for sharing some statistical parameters across these different studies. This paper summarises what is known from large-sample theory about when estimators of a common structural parameter from several independent samples can be combined functionally, or more specifically linearly, to obtain an asymptotically efficient estimator from the combined sample. The main idea is that such combination can be done when the separate-sample nuisance parameters, if any exist, vary freely and independently of one another. The issues are illustrated using data from a multi-centre lung cancer clinical trial. Examples are presented to show that separate estimators cannot always be combined in this way, and that the functionally combined separate estimators may have low or 0 efficiency compared to the unified analysis that could be performed by pooling the datasets.


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