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Accurate Directional Inference for Vector Parameters in Linear Exponential Families

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  • A. C. Davison
  • D. A. S. Fraser
  • N. Reid
  • N. Sartori

Abstract

We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose p -value is computed using one-dimensional integration. The work simplifies and develops earlier research on directional tests for continuous models and on higher-order inference for discrete models, and the examples include contingency tables and logistic regression. Examples and simulations illustrate the high accuracy of the method, which we compare with the usual likelihood ratio test and with an adjusted version due to Skovgaard. In high-dimensional settings, such as covariance selection, the approach works essentially perfectly, whereas its competitors can fail catastrophically.

Suggested Citation

  • A. C. Davison & D. A. S. Fraser & N. Reid & N. Sartori, 2014. "Accurate Directional Inference for Vector Parameters in Linear Exponential Families," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 302-314, March.
  • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:505:p:302-314
    DOI: 10.1080/01621459.2013.839451
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    References listed on IDEAS

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    1. A. C. Davison & D. A. S. Fraser & N. Reid, 2006. "Improved likelihood inference for discrete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 495-508, June.
    2. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
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    Cited by:

    1. Jens Ledet Jensen, 2021. "On the Use of Saddlepoint Approximations in High Dimensional Inference," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 379-392, February.
    2. Wong ACM & Zhang S, 2017. "A Directional Approach for Testing Homogeneity of Inverse Gaussian Scale-Like Parameters," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 3(2), pages 34-39, September.
    3. Ana-Maria Staicu, 2017. "Interview with Nancy Reid," International Statistical Review, International Statistical Institute, vol. 85(3), pages 381-403, December.

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