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A new method of calibration for the empirical loglikelihood ratio


  • Tsao, Min


The Chi-square calibration for the empirical loglikelihood ratio refers to the method of approximating quantiles of the finite sample distribution of the empirical loglikelihood ratio with that of the limiting Chi-square distribution. Empirical likelihood ratio confidence regions are usually computed with the Chi-square calibration. Such Chi-square calibrated confidence regions can have a serious undercoverage problem. This paper examines the undercoverage problem from a finite sample standpoint and proposes a method of calibration which approximates the finite sample distributions with a new family of distributions. The new distributions is another family of sampling distributions arising from the normal distributions and is derived through a simple finite sample similarity between the empirical and parametric likelihoods. The new method of calibration is as easy to use as the Chi-square calibration. It corrects the undercoverage problem of the Chi-square calibration and is consistently more accurate.

Suggested Citation

  • Tsao, Min, 2004. "A new method of calibration for the empirical loglikelihood ratio," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 305-314, July.
  • Handle: RePEc:eee:stapro:v:68:y:2004:i:3:p:305-314

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    References listed on IDEAS

    1. Tsao, Min, 2001. "A small sample calibration method for the empirical likelihood ratio," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 41-45, August.
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    Cited by:

    1. Yongcheng Qi, 2010. "On the tail index of a heavy tailed distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(2), pages 277-298, April.


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