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Biometrika 1995 82(3):489-499; doi:10.1093/biomet/82.3.489
© 1995 by Biometrika Trust
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Stable and invariant adjusted profile likelihood and directed likelihood for curved exponential models

O. E. BARNDORFF-NIELSEN

Department of Theoretical Statistics, Institute of Mathematics, University of Aarhus Ny Munkegade, DK-8000 Aarhus C, Denmark

Received for publication 1 May 1993. Revision received 1 February 1995.
  Abstract

For curved exponential models, the modified profile likelihood and the modified directed likelihood are approximated, with error 0(n-1) under ordinary repeated sampling, by explicitly defined and invariant quantities which do not require specification of an ancillary and which are stable in the sense of having the appropriate conditionality property with respect to any reasonable ancillary.

Key Words: Ancillarity • Conditional inference • Exponential transformation models • Modified profile likelihood • Modified directed likelihood


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