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Biometrika 1975 62(3):599-605; doi:10.1093/biomet/62.3.599
© 1975 by Biometrika Trust
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Marginal and conditional sufficiency

D. A. SPROTT

Department of Statistics, University of Waterloo Ontario

The concepts of sufficiency and ancillarity are extended to marginal and conditional sufficiency in the presence of nuisance parameters. It is required that under the assumption of the absence of knowledge of the nuisance parameter ß no information shall be lost in basing inferences about {Theta} on a statistic that is marginally or conditionally sufficient for {Theta}. The approach is based on the likelihood function and relates the two previously studied apparently dissimilar structures of (a) the factorization of the likelihood and (b) group sufficiency. Some examples are given and the final example illustrates a possible loss of information entailed by the use of statistics that are not marginally or conditionally sufficient.

Key Words: Group sufficiency • Information • Marginal and conditional likelihood • Nuisance parameter • Relative likelihood • Sufficient and ancillary statistics


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