A new method of calibration for the empirical loglikelihood ratio
AbstractThe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 68 (2004)
Issue (Month): 3 (July)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- E - Macroeconomics and Monetary Economics
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- Tsao, Min, 2001. "A small sample calibration method for the empirical likelihood ratio," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 41-45, August.
- Yongcheng Qi, 2010. "On the tail index of a heavy tailed distribution," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(2), pages 277-298, April.
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