Skip to main content
Log in

An extension of the conditional likelihood ratio test to the general multiparameter case

  • Tests
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

In a set-up, where both the interest parameter and the nuisance parameter are possibly multi-dimensional and global parametric orthogonality may not hold, we suggest a test that is superior to the usual likelihood ratio test with regard to second-order local maximinity. The test can be motivated from the principles of conditional and adjusted likelihood.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Amari, S. (1985).Differential Geometrical Methods in Statistics, Springer, New York.

    Google Scholar 

  • Barndorff-Nielsen, O. E. (1986). Inference on full or partial parameters based on the standardized log-likelihood ratio,Biometrika,73, 307–322.

    Google Scholar 

  • Chandra, T. K. and Ghosh, J. K. (1979). Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables,Sankhyā Ser. A,41, 22–47.

    Google Scholar 

  • Chandra, T. K. and Ghosh, J. K. (1980). Valid asymptotic expansions for the likelihood ratio and other statistics under contiguous alternatives,Sankhyā Ser. A,42, 170–184.

    Google Scholar 

  • Conniffe, D. (1990). Testing hypotheses with estimated scores,Biometrika,77, 97–106.

    Google Scholar 

  • Cordeiro, G. M. and McCullagh, P. (1991). Bias correction in generalized linear models,J. Roy. Statist. Soc. Ser. B,53, 629–643.

    Google Scholar 

  • Cox, D. R. (1988). Some aspects of conditional and asymptotic inference: A review,Sankhyā Ser. A,50, 314–337.

    Google Scholar 

  • Cox, D. R. and Reid, N. (1987). Parameter orthogonality and approximate conditional inference (with discussion),J. Roy. Statist. Soc. Ser. B,49, 1–39.

    Google Scholar 

  • Cox, D. R. and Snell, E. J. (1968). A general definition of residuals (with discussion),J. Roy. Statist. Soc. Ser. B,30, 248–275.

    Google Scholar 

  • Ghosh, J. K. and Mukerjee, R. (1992). Bayesian and frequentist Bartlett corrections for likelihood ratio and conditional likelihood ratio tests,J. Roy. Statist. Soc. Ser. B,54, 867–875.

    Google Scholar 

  • Godambe, V. P. (1991). Orthogonality of estimating functions and nuisance parameters,Biometrika,78, 143–151.

    Google Scholar 

  • Harris, P. and Peers, H. W. (1980). The local power of the efficient scores test statistic,Biometrika,67, 525–529.

    Google Scholar 

  • Hayakawa, T. (1975). The likelihood ratio criterion for a composite hypothesis under a local alternative,Biometrika,62, 451–460.

    Google Scholar 

  • Hayakawa, T. (1977). The likelihood ratio criterion and the asymptotic expansion of its distribution,Ann. Inst. Statist. Math.,29, 359–378.

    Google Scholar 

  • Liang, K. Y. (1987). Estimating functions and approximate conditional likelihood,Biometrika,74, 695–702.

    Google Scholar 

  • McCullagh, P. (1987).Tensor Methods in Statistics, Chapman and Hall, London.

    Google Scholar 

  • McCullagh, P. and Tibshirani, R. (1990). A simple method for the adjustment of profile likelihoods,J. Roy. Statist. Soc. Ser. B,52, 325–344.

    Google Scholar 

  • Mukerjee, R. (1992a). Comparison between the conditional likelihood ratio and the usual likelihood ratio tests,J. Roy. Statist. Soc. Ser. B,54, 189–194.

    Google Scholar 

  • Mukerjee, R. (1992b). Conditional likelihood and power: Higher order asymptotics,Proc. Roy. Soc. London Ser. A,438, 433–446.

    Google Scholar 

  • Mukerjee, R. and Chandra, T. K. (1991). Bartlett-type adjustment for the conditional likelihood ratio statistic of Cox and Reid,Biometrika,78, 365–372.

    Google Scholar 

  • Peers, H. W. (1971). Likelihood ratio and associated test criteria,Biometrika,58, 477–487.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Mukerjee, R. An extension of the conditional likelihood ratio test to the general multiparameter case. Ann Inst Stat Math 45, 759–771 (1993). https://doi.org/10.1007/BF00774786

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00774786

Key words and phrases

Navigation