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

Jonker Marianne () and Aad Van der Vaart ()
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Jonker Marianne: Department of Epidemiology and Biostatistics, VUmc, Postbus 7057 1007 MB, Amsterdam, The Netherlands
Aad Van der Vaart: Mathematical Institute, Leiden University, Leiden, The Netherlands

The International Journal of Biostatistics, 2014, vol. 10, issue 2, 123-142

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.

Keywords: likelihood ratio test; nuisance parameters; testing; test level; chi-squared distribution (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/ijb-2013-0063

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