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On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source

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  • Jonker Marianne

    (Department of Epidemiology and Biostatistics, VUmc, Postbus 7057 1007 MB, Amsterdam, The Netherlands)

  • Van der Vaart Aad

    (Mathematical Institute, Leiden University, Leiden, The Netherlands)

Abstract

In practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low. In this article, we derive the asymptotic distribution of the likelihood ratio statistic if the nuisance parameters are estimated based on a dataset that is independent of the data used for estimating the parameter of interest. This distribution can be used for correctly testing hypotheses and constructing confidence intervals. Four theoretical and practical examples are given as illustration.

Suggested Citation

  • Jonker Marianne & Van der Vaart Aad, 2014. "On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 1-20, November.
    • Handle: RePEc:bpj:ijbist:v:10:y:2014:i:2:p:20:n:8
    DOI: 10.1515/ijb-2013-0063
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    References listed on IDEAS

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    1. Qin, Gengsheng & Jing, Bing-Yi, 2001. "Censored Partial Linear Models and Empirical Likelihood," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 37-61, July.
    2. Qi-Hua Wang & Bing-Yi Jing, 2001. "Empirical Likelihood for a Class of Functionals of Survival Distribution with Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(3), pages 517-527, September.
    3. Gengsheng Qin & Bing‐Yi Jing, 2001. "Empirical Likelihood for Censored Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 661-673, December.
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