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On Sprott's Example of an Ancillary Statistic

Published online by Cambridge University Press:  20 November 2018

Peter Tan
Peter Tan*
Affiliation:
Carleton University, Ottawa, Ontario
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For statistical inference on the unknown parameter θ of a probability distribution with a known form of its density function f(x | θ), the late Sir R. A. Fisher suggests that inference should be based on the observed value of a sufficient statistic when it exists. In the absence of a sufficient statistic, fiducial probability statements about θ can still be made, according to Fisher, if we can find an ancillary statistic so that "the most likely estimate could be made exhaustive by means of the ancillary values" [1, p. 138].

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 2 , June 1970, pp. 205 - 207
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Fisher, R. A., Statistical methods and scientific inference, Oliver and Boyd, Edinburgh (second edition), 1959.Google Scholar
2. Dempster, A. P., Elements of continuous multivariate analysis, Addison-Wesley, Reading, Mass., 1969.Google Scholar
3. Sprott, D. A., An example of an ancillary statistic and the combination of two samples by Bayes' Theorem, Ann. Math. Stat. 32 (1961), 616-618.Google Scholar
4. Fraser, D. A. S., The structure of inference, Wiley, New York, 1968.Google Scholar
5. Fraser, D. A. S., On sufficiency and conditional sufficiency, Sankhyā A 28 (1966), 145-150.Google Scholar