Editing Statistical inference (section)

====Structural inference====

Developing ideas of Fisher and of Pitman from 1938 to 1939,<ref>Davison, page 12. {{full citation needed|date=November 2012}}</ref> [[George A. Barnard]] developed "structural inference" or "pivotal inference",<ref>Barnard, G.A. (1995) "Pivotal Models and the Fiducial Argument", International Statistical Review, 63 (3), 309–323. {{JSTOR|1403482}}</ref> an approach using [[Haar measure|invariant probabilities]] on [[group family|group families]]. Barnard reformulated the arguments behind fiducial inference on a restricted class of models on which "fiducial" procedures would be well-defined and useful. [[Donald A. S. Fraser]] developed a general theory for structural inference<ref>{{Cite book|last=Fraser|first=D. A. S.|url=https://www.worldcat.org/oclc/440926|title=The structure of inference|date=1968|publisher=Wiley|isbn=0-471-27548-4|location=New York|oclc=440926}}</ref> based on [[group theory]] and applied this to linear models.<ref>{{Cite book|last=Fraser|first=D. A. S.|url=https://www.worldcat.org/oclc/3559629|title=Inference and linear models|date=1979|publisher=McGraw-Hill|isbn=0-07-021910-9|location=London|oclc=3559629}}</ref> The theory formulated by Fraser has close links to decision theory and Bayesian statistics and can provide optimal frequentist decision rules if they exist.<ref>{{Cite journal|last1=Taraldsen|first1=Gunnar|last2=Lindqvist|first2=Bo Henry|date=2013-02-01|title=Fiducial theory and optimal inference|url=https://projecteuclid.org/journals/annals-of-statistics/volume-41/issue-1/Fiducial-theory-and-optimal-inference/10.1214/13-AOS1083.full|journal=The Annals of Statistics|volume=41|issue=1|doi=10.1214/13-AOS1083|arxiv=1301.1717|s2cid=88520957|issn=0090-5364}}</ref>