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Likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative

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  • Christian Ritz
  • Ib M. Skovgaard

Abstract

For submodels of an exponential family, we consider likelihood ratio tests for hypotheses that render some parameters nonidentifiable. First, we establish the asymptotic equivalence between the likelihood ratio test and the score test. Secondly, the score-test representation is used to derive the asymptotic distribution of the likelihood ratio test. These results are derived for general submodels of an exponential family without assuming compactness of the parameter space. We then exemplify the results on a class of multivariate normal models, where null hypotheses concerning the covariance structure lead to loss of identifiability of a parameter. Our motivating problem throughout the paper is to test a random intercepts model against an alternative covariance structure allowing for serial correlation. Copyright 2005, Oxford University Press.

Suggested Citation

  • Christian Ritz & Ib M. Skovgaard, 2005. "Likelihood ratio tests in curved exponential families with nuisance parameters present only under the alternative," Biometrika, Biometrika Trust, vol. 92(3), pages 507-517, September.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:507-517
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    File URL: http://hdl.handle.net/10.1093/biomet/92.3.507
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    Cited by:

    1. Wei‐Wen Hsu & David Todem & KyungMann Kim, 2016. "A sup‐score test for the cure fraction in mixture models for long‐term survivors," Biometrics, The International Biometric Society, vol. 72(4), pages 1348-1357, December.
    2. Wei-Wen Hsu & David Todem & Kyungmann Kim, 2015. "Adjusted Supremum Score-Type Statistics for Evaluating Non-Standard Hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 746-759, September.
    3. C. Baayen & P. Hougaard & C. B. Pipper, 2015. "Testing effect of a drug using multiple nested models for the dose–response," Biometrics, The International Biometric Society, vol. 71(2), pages 417-427, June.
    4. Christian Ritz, 2013. "Penalized likelihood ratio tests for repeated measurement models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 534-547, September.
    5. Guanqun Cao & David Todem & Lijian Yang & Jason P. Fine, 2013. "Evaluating Statistical Hypotheses Using Weakly-Identifiable Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 256-273, June.

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