## Abstract

Consider a model with parameter = (, ), where is the parameter of interest, and let L(, ) denote the likelihood function. One approach to likelihood inference for is to use an integrated likelihood function, in which is eliminated from L(, ) by integrating with respect to a density function (|). The goal of this paper is to consider the problem of selecting (|) so that the resulting integrated likelihood function is useful for non-Bayesian likelihood inference. The desirable properties of an integrated likelihood function are analyzed and these suggest that (|) should be chosen by finding a nuisance parameter that is unrelated to and then taking the prior density for to be independent of . Such an unrelated parameter is constructed and the resulting integrated likelihood is shown to be closely related to the modified profile likelihood.

Original language | English (US) |
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Pages (from-to) | 524-542 |

Number of pages | 19 |

Journal | Biometrika |

Volume | 94 |

Issue number | 3 |

DOIs | |

State | Published - Sep 14 2007 |

## Keywords

- Modified profile likelihood
- Nuisance parameter
- Orthogonal parameters
- Reference prior

## ASJC Scopus subject areas

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