Saddlepoint approximation for the distribution of the modified signed root of likelihood ratio statistics near the mean

Juan Zhang, John Kolassa

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)194-203
Number of pages10
JournalCommunications in Statistics - Theory and Methods
Volume37
Issue number2
DOIs
StatePublished - Jan 1 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

Keywords

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

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