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

Andreï Kostyrka ()
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Andreï Kostyrka: DEM, Université du Luxembourg

DEM Discussion Paper Series from Department of Economics at the University of 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.

Keywords: empirical likelihood; convex hull; moment-condition models; extrapolation and splicing; radial reduction (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:luc:wpaper:25-19

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