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Extrapolated empirical likelihood as a solution to the convex-hull-violation problem

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  • Andreï Kostyrka

    (DEM, Université du Luxembourg)

Abstract

Empirical likelihood (EL) breaks down when the hypothesised mean falls outside the convex hull of the sample. We propose extrapolated EL (ExEL) – two splicing schemes that extend the log-EL ratio beyond the hull while leaving it unchanged on a user-chosen interior region. The first scheme, ExEL1, continues EL past a data-driven cut-off using its local quadratic (Taylor) expansion. The second scheme, ExEL2, smoothly splices EL to its globalWald quadratic approximation via a convex bridge. Both methods extend naturally to multiple dimensions by radial reduction. In simulations with small samples – where convex-hull violations are common – ExEL remains well-behaved and distinguishes mild from severe violations. It also has attractive inferential properties, delivering accurate coverage probabilities with bootstrap calibration.

Suggested Citation

  • Andreï Kostyrka, 2025. "Extrapolated empirical likelihood as a solution to the convex-hull-violation problem," DEM Discussion Paper Series 25-19, Department of Economics at the University of Luxembourg.
    • Handle: RePEc:luc:wpaper:25-19
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    File URL: https://orbilu.uni.lu/handle/10993/66943
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    References listed on IDEAS

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    1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    2. 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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