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On empirical likelihood statistical functions

Author

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  • Yuan, Ao
  • Xu, Jinfeng
  • Zheng, Gang

Abstract

We consider the empirical likelihood method for estimation of distribution and quantile functions where side information is incorporated through moment conditions. We systematically study the asymptotic properties of the estimators, such as the uniform strong laws of large numbers and weak convergence over classes of functions. Two Monte Carlo examples are also given to illustrate the practical utility of the method.

Suggested Citation

  • Yuan, Ao & Xu, Jinfeng & Zheng, Gang, 2014. "On empirical likelihood statistical functions," Journal of Econometrics, Elsevier, vol. 178(P3), pages 613-623.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p3:p:613-623
    DOI: 10.1016/j.jeconom.2013.08.037
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    References listed on IDEAS

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    1. Biao Zhang, 1997. "Quantile Processes in the Presence of Auxiliary Information," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 35-55, March.
    2. Imbens, Guido W, 2002. "Generalized Method of Moments and Empirical Likelihood," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 493-506, October.
    3. Gianfranco Adimari, 1997. "Empirical Likelihood Type Confidence Intervals Under Random Censorship," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 447-466, September.
    4. Yuichi Kitamura & Gautam Tripathi & Hyungtaik Ahn, 2004. "Empirical Likelihood-Based Inference in Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 72(6), pages 1667-1714, November.
    5. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    6. Jing Qin & Biao Zhang, 2005. "Marginal likelihood, conditional likelihood and empirical likelihood: Connections and applications," Biometrika, Biometrika Trust, vol. 92(2), pages 251-270, June.
    7. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    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.
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    Cited by:

    1. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.

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    More about this item

    Keywords

    Empirical likelihood; Quantile estimation; Uniform SLLN; Uniform CLT;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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