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Edgeworth expansions for GEL estimators

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  • Kundhi, Gubhinder
  • Rilstone, Paul

Abstract

Finite sample approximations for the distribution functions of Generalized Empirical Likelihood (GEL) are derived using Edgeworth expansions. The analytical results obtained are shown to apply to most of the common extremum estimators used in applied work in an i.i.d. sampling context. The GEL estimators considered include the Continuous Updating, Empirical Likelihood and Exponential Tilting estimators. These estimators are popular alternatives to Generalized Method of Moment (GMM) estimators and their finite sample properties are examined. In a Monte Carlo Experiment, higher order analytical corrections provided by Edgeworth approximations work well in comparison to first order approximations and improve inferences in finite samples.

Suggested Citation

  • Kundhi, Gubhinder & Rilstone, Paul, 2012. "Edgeworth expansions for GEL estimators," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 118-146.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:118-146
    DOI: 10.1016/j.jmva.2011.11.005
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    1. Lee, Seojeong, 2016. "Asymptotic refinements of a misspecification-robust bootstrap for GEL estimators," Journal of Econometrics, Elsevier, vol. 192(1), pages 86-104.
    2. Gubhinder Kundhi & Paul Rilstone, 2020. "Simplified Matrix Methods for Multivariate Edgeworth Expansions," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(2), pages 293-326, June.
    3. La Vecchia, Davide & Moor, Alban & Scaillet, Olivier, 2023. "A higher-order correct fast moving-average bootstrap for dependent data," Journal of Econometrics, Elsevier, vol. 235(1), pages 65-81.
    4. Yong Bao & Aman Ullah, 2021. "Analytical Finite Sample Econometrics: From A. L. Nagar to Now," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 17-37, December.
    5. Gubhinder Kundhi & Paul Rilstone, 2015. "Saddlepoint expansions for GEL estimators," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 1-24, March.
    6. Seojeong Lee, 2018. "Asymptotic Refinements of a Misspecification-Robust Bootstrap for Generalized Empirical Likelihood Estimators," Papers 1806.00953, arXiv.org, revised Jun 2018.
    7. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.

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