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Theory & Methods: On the Order of Data Reductions by Ancillarity and by Sufficiency
Author(s) -
Kabaila Paul
Publication year - 2001
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00176
Subject(s) - frequentist inference , statistic , mathematics , inference , statistical inference , context (archaeology) , econometrics , fiducial inference , simple (philosophy) , statistics , reduction (mathematics) , mathematical economics , computer science , artificial intelligence , bayesian inference , bayesian probability , epistemology , paleontology , geometry , biology , philosophy
In the context of frequentist inference there are strong arguments in favour of data reduction by both (a) conditioning on the most appropriate ancillary statistic and (b) restricting attention to a minimal sufficient statistic. However, significantly for the study of the foundations of frequentist inference, there are some examples in which the order of application of these data reductions has an important bearing on the statistical inference of interest. This paper presents a new simple example of this kind.