## Abstract

Barndorff-Nielsen introduced a variable U in the adjusted saddlepoint approximation (R)+(R)(R-1-U-1) to reduce the order of error in the standard normal approximation to the distribution of the log-likelihood ratio statistic R. DiCiccio and Martin (1993) proposed a modification, which avoids the practical difficulties of finding an exact or approximate ancillary A in calculating Barndorff-Nielsen's variable U. We repair the numerical difficulties in applying their modification, when the ordinate at which the approximation is evaluated is near the conditional mean of the approximated distribution. Some special cases and examples are discussed.

Original language | English (US) |
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Pages (from-to) | 194-203 |

Number of pages | 10 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 37 |

Issue number | 2 |

DOIs | |

State | Published - Jan 2008 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability

## Keywords

- Conditional inference
- Linear approximation
- Saddlepoint approxi-mation
- Signed likelihood ratio statistic
- Singularity