## Abstract

SUMMARY: The general problem of inference about a scalar parameter of interest θ in the presence of a nuisance parameter λ using conditional inference is considered.xml. A condition is given under which inference based on the conditional distribution of θ, the maximum likelihood estimate of θ, given λ_{o}, the maximum likelihood estimate of λ for fixed θ = θ_{0}, is optimal, in a certain sense. When this condition is not satisfied, it is shown that inference should be based on the conditional distribution of θ given λ_{o}, j_{o} where j_{o} denotes the observed information for λ for fixed θ =θθ_{o}, although this will involve some loss of information about θ. This information loss is shown to be related to the statistical curvature of the model.

Original language | English (US) |
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Pages (from-to) | 649-661 |

Number of pages | 13 |

Journal | Biometrika |

Volume | 81 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1994 |

## Keywords

- Asymptotic theory
- Conditional inference
- Information
- Likelihood inference
- Local inference
- Observed information
- Statistical curvature

## ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Mathematics(all)
- Statistics and Probability
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)