Small-sample confidence regions in exponential families

John E. Kolassa*, Martin A Tanner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This article presents an algorithm for small-sample conditional confidence regions for two or more parameters for any discrete regression model in the generalized linear interactive model family. Regions are constructed by careful inversion of conditional hypothesis tests. This method presupposes the use of approximate or exact techniques for enumerating the sample space for some components of the vector of sufficient statistics conditional on other components. Such enumeration may be performed exactly or by exact or approximate Monte Carlo, including the algorithms of Kolassa and Tanner (1994, Journal of the American Statistical Association 89, 697-702; 1999, Biometrics 55, 246-251). This method also assumes that one can compute certain conditional probabilities for a fixed value of the parameter vector. Because of a property of exponential families, one can use this set of conditional probabilities to directly compute the conditional probabilities associated with any other value of the vector of the parameters of interest. This observation dramatically reduces the computational effort required to invert the hypothesis test to obtain the confidence region. To construct a region with confidence level 1 - α, the algorithm begins with a grid of values for the parameters of interest. For each parameter vector on the grid (corresponding to the current null hypothesis), one transforms the initial set of conditional probabilities using exponential tilting and then calculates the p value for this current null hypothesis. The confidence region is the set of parameter values for which the p value is at least α.

Original languageEnglish (US)
Pages (from-to)1291-1294
Number of pages4
JournalBiometrics
Volume55
Issue number4
DOIs
StatePublished - Jan 1 1999

Keywords

  • Conditional inference
  • Monte Carlo
  • Saddlepoint approximations

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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