Advertisement

Statistical Papers

, 31:83 | Cite as

Views on conditional and marginal methods of statistical inference

  • D. A. S. Fraser
Articles

Abstract

Conditional and marginal likelihood analysis has a long history of development. Some recent methods using exact and approximate density and distribution functions lead to more sharply defined likelihoods and to accurate observed levels of significance for a wide range of problems including nonnormal regression and exponential linear models. These developments will be surveyed.

Keywords

Conditional Distribution Marginal Distribution Transformation Model Nuisance Parameter Marginal Likelihood 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Barndorff-Nielsen, O.E. (1983). On a formula for the distribution of the maximum likelihood estimator. Biometrika70, 343–365.MATHCrossRefMathSciNetGoogle Scholar
  2. Barndorff-Nielsen, O.E. and D.R. Cox (1979). Edgeworth and saddlepoint approximations with statistical applications. J. Roy. Statist. Soc. B41, 279–312.MATHMathSciNetGoogle Scholar
  3. Cox, D.R. and N. Reid (1987). Parameter orthogonality and approximate conditional inference (with discussion). J. Royal Statist. Soc. B49, 1–36.MATHMathSciNetGoogle Scholar
  4. Daniels, H. (1954). Saddlepoint approximations in statistics. Ann. Math. Statist.25, 631–650.CrossRefMathSciNetMATHGoogle Scholar
  5. Fraser, D.A.S. (1967). Data transformations and the linear model. Annals Math. Statist.38, 1456–1465.CrossRefMathSciNetMATHGoogle Scholar
  6. Fraser, D.A.S. (1968). The Structure of Inference. New York: Wiley, Toronto: DAI.MATHGoogle Scholar
  7. Fraser, D.A.S. (1979). Inference and Linear Models. New York: McGraw Hill, Toronto: DAI.MATHGoogle Scholar
  8. Fraser, D.A.S. (1987). Sequential parameter structure, conditional inference, and likelihood drop. Statist. Papers28, 27–52.MATHMathSciNetGoogle Scholar
  9. Fraser, D.A.S. and N. Reid (1988a). On comparing two methods for approximate conditional inference. Statist. Papers29, 271–280.MATHMathSciNetCrossRefGoogle Scholar
  10. Fraser, D.A.S. and N. Reid (1988b). Fibre analysis and conditional inference. Statistical Theory and Data Analysis (Ed.: K. Matusita), 241–247, Amsterdam: North Holland.Google Scholar
  11. Fraser, D.A.S. and N. Reid (1988c). On conditional inference for a real parameter: a differential approach on the sample space, Biometrika 75, 251–264.MATHCrossRefMathSciNetGoogle Scholar
  12. Peisakoff, M. (1951). Transformation parameters. Ph.D. thesis, Princeton University.Google Scholar
  13. Kalbfleisch, J.D. and D.A. Sprott (1970). Application of likelihood methods to models involving large numbers of parameters. Jour. Roy Statist. Soc. B 32, 175–208.MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • D. A. S. Fraser
    • 1
  1. 1.Department of MathematicsYork UniversityNorth YorkCanada

Personalised recommendations