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Bartlett correctable two-sample adjusted empirical likelihood

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  • Liu, Yukun
  • Yu, Chi Wai

Abstract

We propose a two-sample adjusted empirical likelihood (AEL) to construct confidence regions for the difference of two d-dimensional population means. This method eliminates the non-definition of the usual two-sample empirical likelihood (EL) and is shown to be Bartlett correctable. We further show that when the adjustment level is half the Bartlett correction factor for the usual two-sample EL, the two-sample AEL has the same high-order precision as the EL with Bartlett correction. To enhance the performance of the two-sample AEL with adjustment level being half the Bartlett correction factor, we propose a less biased estimate of the Bartlett correction factor. The efficiency of the proposed method is illustrated by simulations and a real data example.

Suggested Citation

  • Liu, Yukun & Yu, Chi Wai, 2010. "Bartlett correctable two-sample adjusted empirical likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1701-1711, August.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:7:p:1701-1711
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    References listed on IDEAS

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    1. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    2. Chen, S. X., 1994. "Empirical Likelihood Confidence Intervals for Linear Regression Coefficients," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 24-40, April.
    3. Liu, Yukun & Zou, Changliang & Zhang, Runchu, 2008. "Empirical likelihood for the two-sample mean problem," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 548-556, April.
    4. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, vol. 141(2), pages 492-516, December.
    5. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
    6. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, vol. 93(1), pages 215-220, March.
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    Cited by:

    1. Tsao, Min & Wu, Fan, 2015. "Two-sample extended empirical likelihood for estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 1-15.
    2. Kun Chen & Ngai Hang Chan & Chun Yip Yau, 2020. "Bartlett correction of frequency domain empirical likelihood for time series with unknown innovation variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1159-1173, October.
    3. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.
    4. Yukun Liu & Changliang Zou & Zhaojun Wang, 2013. "Calibration of the empirical likelihood for high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 529-550, June.
    5. Varron, Davit, 2016. "Empirical likelihood confidence tubes for functional parameters in plug-in estimation," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 100-118.
    6. Wu, Fan & Tsao, Min, 2014. "Two-sample extended empirical likelihood," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 81-87.
    7. Ramadha D. Piyadi Gamage & Wei Ning, 2020. "Inference for short‐memory time series models based on modified empirical likelihood," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(3), pages 322-339, September.
    8. Ramadha D. Piyadi Gamage & Wei Ning & Arjun K. Gupta, 2017. "Adjusted Empirical Likelihood for Time Series Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 336-360, November.

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