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Two-sample extended empirical likelihood for estimating equations

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  • Tsao, Min
  • Wu, Fan

Abstract

We propose a two-sample extended empirical likelihood for inference on the difference between two p-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett correctable but its domain is a bounded subset of the parameter space. We expand its domain through a composite similarity transformation to derive the two-sample extended empirical likelihood which is defined on the full parameter space. The extended empirical likelihood has the same asymptotic distribution as the standard one and can also achieve the second-order accuracy of the Bartlett correction. We include two applications to illustrate the use of two-sample empirical likelihood methods and to demonstrate the superior coverage accuracy of the extended empirical likelihood confidence regions.

Suggested Citation

  • Tsao, Min & Wu, Fan, 2015. "Two-sample extended empirical likelihood for estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 1-15.
    • Handle: RePEc:eee:jmvana:v:142:y:2015:i:c:p:1-15
    DOI: 10.1016/j.jmva.2015.07.009
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    References listed on IDEAS

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    1. Xuemin Zi & Changliang Zou & Yukun Liu, 2012. "Two-sample empirical likelihood method for difference between coefficients in linear regression model," Statistical Papers, Springer, vol. 53(1), pages 83-93, February.
    2. Min Tsao & Fan Wu, 2014. "Extended empirical likelihood for estimating equations," Biometrika, Biometrika Trust, vol. 101(3), pages 703-710.
    3. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    4. Qin, Yongsong & Rao, J.N.K. & Wu, Changbao, 2010. "Empirical likelihood confidence intervals for the Gini measure of income inequality," Economic Modelling, Elsevier, vol. 27(6), pages 1429-1435, November.
    5. Wen‐Hao Chen, 2009. "Cross‐National Differences In Income Mobility: Evidence From Canada, The United States, Great Britain And Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(1), pages 75-100, March.
    6. David Domeij & Martin Floden, 2010. "Inequality Trends in Sweden 1978-2004," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(1), pages 179-208, January.
    7. 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.
    8. 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.
    9. 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.
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    Cited by:

    1. Federico Crudu, 2017. "Errors-in-Variables Models with Many Proxies," Department of Economics University of Siena 774, Department of Economics, University of Siena.

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