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Finite-sample properties of the adjusted empirical likelihood

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  • Jiahua Chen
  • Yi Huang

Abstract

Empirical likelihood-based confidence intervals for the population mean have many interesting properties [Owen, A.B. (1988), 'Empirical Likelihood Ratio Confidence Intervals for a Single Functional', Biometrika , 75, 237-249]. Calibrated by χ-super-2 limiting distribution, however, their coverage probabilities are often lower than the nominal when the sample size is small and/or the dimension of the data is high. The application of adjusted empirical likelihood (AEL) is one of the many ways to achieve a more accurate coverage probability. In this paper, we study the finite-sample properties of the AEL. We find that the AEL ratio function decreases when the level of adjustment increases. Thus, the AEL confidence region has higher coverage probabilities when the level of adjustment increases. We also prove that the AEL ratio function increases when the putative population mean moves away from the sample mean. In addition, we show that the AEL confidence region for the population mean is convex. Finally, computer simulations are conducted to further investigate the precision of the coverage probabilities and the sizes of the confidence regions. An application example is also included.

Suggested Citation

  • Jiahua Chen & Yi Huang, 2013. "Finite-sample properties of the adjusted empirical likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 147-159, March.
    • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:1:p:147-159
    DOI: 10.1080/10485252.2012.738906
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    Cited by:

    1. Min Tsao & Fan Wu, 2014. "Extended empirical likelihood for estimating equations," Biometrika, Biometrika Trust, vol. 101(3), pages 703-710.
    2. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2017. "Empirical likelihood ratio in penalty form and the convex hull problem," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 507-529, November.
    3. Nicola Lunardon & Gianfranco Adimari, 2016. "Second-order Accurate Confidence Regions Based on Members of the Generalized Power Divergence Family," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 213-227, March.
    4. Henry Lam, 2019. "Recovering Best Statistical Guarantees via the Empirical Divergence-Based Distributionally Robust Optimization," Operations Research, INFORMS, vol. 67(4), pages 1090-1105, July.
    5. Xianyang Zhang & Xiaofeng Shao, 2016. "On the coverage bound problem of empirical likelihood methods for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 395-421, March.

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