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Likelihood ratio statistics based on an integrated likelihood

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  • T. A. Severini

Abstract

An integrated likelihood depends only on the parameter of interest and the data, so it can be used as a standard likelihood function for likelihood-based inference. In this paper, the higher-order asymptotic properties of the signed integrated likelihood ratio statistic for a scalar parameter of interest are considered. These results are used to construct a modified integrated likelihood ratio statistic and to suggest a class of prior densities to use in forming the integrated likelihood. The properties of the integrated likelihood ratio statistic are compared to those of the standard likelihood ratio statistic. Several examples show that the integrated likelihood ratio statistic can be a useful alternative to the standard likelihood ratio statistic. Copyright 2010, Oxford University Press.

Suggested Citation

  • T. A. Severini, 2010. "Likelihood ratio statistics based on an integrated likelihood," Biometrika, Biometrika Trust, vol. 97(2), pages 481-496.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:481-496
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    File URL: http://hdl.handle.net/10.1093/biomet/asq015
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    Citations

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    Cited by:

    1. Zhenyu Zhao & Thomas A. Severini, 2017. "Integrated likelihood computation methods," Computational Statistics, Springer, vol. 32(1), pages 281-313, March.
    2. Giuliana Cortese & Nicola Sartori, 2016. "Integrated likelihoods in parametric survival models for highly clustered censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 382-404, July.
    3. H. V. Kulkarni & S. M. Patil, 2021. "Uniformly implementable small sample integrated likelihood ratio test for one-way and two-way ANOVA under heteroscedasticity and normality," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 273-305, June.
    4. Thomas A. Severini, 2023. "Integrated likelihood inference in multinomial distributions," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 131-142, August.
    5. Zaigraev, A. & Podraza-Karakulska, A., 2014. "Maximum integrated likelihood estimator of the interest parameter when the nuisance parameter is location or scale," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 99-106.
    6. Briceön Wiley & Chris Elrod & Phil D. Young & Dean M. Young, 2021. "An integrated‐likelihood‐ratio confidence interval for a proportion based on underreported and infallible data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 290-298, August.
    7. Ruggero Bellio & Annamaria Guolo, 2016. "Integrated Likelihood Inference in Small Sample Meta-analysis for Continuous Outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 191-201, March.

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