## Abstract

The likelihood ratio approximation, also called Barndorff-Nielsen's approximation and often denoted by p*, provides a highly accurate approximation to the conditional density of a maximum likelihood estimator θ̂ given an ancillary statistic. In this paper, the properties of p* are considered for the case in which the underlying random variables have a lattice distribution and θ̂ has a discrete, but not necessarily lattice, distribution. If θ̂ has a lattice distribution, then p* provides a valid approximation to the density of θ̂ with respect to counting measure. If the distribution of θ̂ is non-lattice, then p* is still a valid approximation to the conditional density of θ̂; however, the dominating measure is no longer counting measure.

Original language | English (US) |
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Pages (from-to) | 939-945 |

Number of pages | 7 |

Journal | Biometrika |

Volume | 87 |

Issue number | 4 |

DOIs | |

State | Published - 2000 |

## Keywords

- Ancillary statistic
- Asymptotic theory
- Lattice distribution
- Likelihood
- Maximum likelihood estimator

## ASJC Scopus subject areas

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