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Small sample inference for probabilistic index models

Author

Listed:
  • Amorim, G.
  • Thas, O.
  • Vermeulen, K.
  • Vansteelandt, S.
  • De Neve, J.

Abstract

Probabilistic index models may be used to generate classical and new rank tests, with the additional advantage of supplementing them with interpretable effect size measures. The popularity of rank tests for small sample inference makes probabilistic index models also natural candidates for small sample studies. However, at present, inference for such models relies on asymptotic theory that can deliver poor approximations of the sampling distribution if the sample size is rather small. A bias-reduced version of the bootstrap and adjusted jackknife empirical likelihood are explored. It is shown that their application leads to drastic improvements in small sample inference for probabilistic index models, justifying the use of such models for reliable and informative statistical inference in small sample studies.

Suggested Citation

  • Amorim, G. & Thas, O. & Vermeulen, K. & Vansteelandt, S. & De Neve, J., 2018. "Small sample inference for probabilistic index models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 137-148.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:137-148
    DOI: 10.1016/j.csda.2017.11.005
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    References listed on IDEAS

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    1. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. Jan De Neve & Olivier Thas, 2015. "A Regression Framework for Rank Tests Based on the Probabilistic Index Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1276-1283, September.
    3. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.
    4. Olivier Thas & Jan De Neve & Lieven Clement & Jean-Pierre Ottoy, 2012. "Probabilistic index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(4), pages 623-671, September.
    5. Li, Minqiang & Peng, Liang & Qi, Yongcheng, 2011. "Reduce computation in profile empirical likelihood method," MPRA Paper 33744, University Library of Munich, Germany.
    6. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
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