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Biometrika 1988 75(2):251-264; doi:10.1093/biomet/75.2.251
© 1988 by Biometrika Trust
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On conditional inference for a real parameter: A differential approach on the sample space

D. A. S. FRASER and N. REID

Department of Mathematics, York University Toronto, M3T 1P3, Canada
Department of Statistics, University of Toronto Toronto M5S 1A1, Canada

A one-dimensional conditional procedure defines a partition of the sample space into curves which can be represented by means of a unit vector field. A formula is given for the conditional distribution in terms of local properties of the vector field. Conditions are developed for reducing the first-order effects of nuisance parameters and reproducing to higher order the likelihood change for the parameter of interest. The emphasis is on extending exponential family methods after locally approximating the statistical model by an exponential family.

Key Words: Ancillary • Differential • Exponential family • Likelihood • Orthogonality • Sample space partition • Sufficiency


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