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Algorithms for approximate conditional inference

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Abstract

This paper presents a method for listing the sample space for a conditional distribution in a discrete generalized linear model. This tabulation is used in conjunction with saddlepoint methods to approximate the associated conditional probabilities. These probabilities are used to calculate conditional p-values.

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References

  • Cytel Software Corporation 1999. LogXact 4 for Windows. Cytel Software Corporation, Cambridge, MA.

    Google Scholar 

  • Daniels H.E. 1954. Saddlepoint approximations in statistics. Annals of Mathematical Statistics 25: 614–649.

    Google Scholar 

  • Davison A.C. 1988. Approximate conditional inference in generalized linear models. Journal of the Royal Statistical Society, Ser. B 50: 445–461.

    Google Scholar 

  • Falsey A., Criddle M.M., Kolassa J.E., McCann R.M., Brower C., and Hall W. 1999. Evaluation of a handwashing intervention to reduce respiratory illness rates in senior day-care centers. Infection Control and Hospital Epidemiology 20: 200–202.

    Google Scholar 

  • Forster J.J., McDonald J.W., and Smith P.W.F. 1996. Monte Carlo exact conditional tests for log-linear and logistic models. Journal of the Royal Statistical Society, Ser. B 58: 445–453.

    Google Scholar 

  • Hirji K.F. 1992. Computing exact distributions for polytomous response data. Journal of the American Statistical Association 87: 487–492.

    Google Scholar 

  • Hirji K.F., Mehta C.R., and Patel N.R. 1987. Computing distributions for exact logistic regression. Journal of the American Statistical Association 82: 1110–1117.

    Google Scholar 

  • Kolassa J.E. 1997. Series Approximation Methods in Statistics (2nd Edn.). Springer-Verlag, New York.

    Google Scholar 

  • Kolassa J.E. 2000. Saddlepoint approximation at the edges of a conditional sample space. Statistics and Probability Letters 50: 343–349.

    Google Scholar 

  • Kolassa J.E. and Tanner M.A. 1994. Approximate conditional inference in exponential families via the Gibbs sampler. Journal of the American Statistical Association 89: 697–702.

    Google Scholar 

  • Kolassa J.E. and Tanner M.A. 1999a. Approximate Monte Carlo conditional inference in exponential families. Biometrics 55: 246–251.

    Google Scholar 

  • Kolassa J.E. and Tanner M.A. 1999b. Small sample confidence regions in exponential families. Biometrics 55: 1291–1294.

    Google Scholar 

  • Lugannani R. and Rice S. 1980. Saddle point approximation for the distribution of the sum of independent random variables. Advances in Applied Probability 12: 475–490.

    Google Scholar 

  • McCullagh P. and Nelder J.A. 1989. Generalized Linear Models. Chapman and Hall, London.

    Google Scholar 

  • Mehta C., Patel N., and Senchaudhuri P. 2000. Efficient Monte Carlo methods for conditional logistic regression. Journal of the American Statistical Association 95: 99–108.

    Google Scholar 

  • Pierce D.A. and Peters D. 1997. Improving exact tests by approximate conditioning. Biometrika 86: 265–277.

    Google Scholar 

  • Reid N. 1988. Saddlepoint methods and statistical inference. Statistical Science 3: 213–238.

    Google Scholar 

  • Routledge R. and Tsao M. 1995. Uniformvalidity of saddlepoint expansion on complex sets. Canadian Journal of Statistics 23: 425–431.

    Google Scholar 

  • Skovgaard I.M. 1987. Saddlepoint expansions for conditional distributions. Journal of Applied Probability 24: 875–887.

    Google Scholar 

  • Skovgaard I.M. 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28: 3–32.

    Google Scholar 

  • Strawderman R.L., Cassella G., and Wells M.T. 1996. Practical smallsample asymptotics for regression problems. Journal of the American Statistical Association 91: 643–654. x

    Google Scholar 

  • Waterman R.P. and Lindsay B.G. 1996. A simple and accurate method for approximate conditional inference in linear exponential family models. Journal of the Royal Statistical Society, Ser. B 58: 177–188.

    Google Scholar 

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Kolassa, J.E. Algorithms for approximate conditional inference. Statistics and Computing 13, 121–126 (2003). https://doi.org/10.1023/A:1023252308207

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  • DOI: https://doi.org/10.1023/A:1023252308207

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