Faculty of Science, Technology and Medicine
Faculty of Law, Economics and Finance
Faculty of Humanities, Education and Social Sciences
Interdisciplinary Centre for Security, Reliability and Trust
Luxembourg Centre for Systems Biomedicine
Luxembourg Centre for Contemporary and Digital History
Luxembourg Centre for European Law
Luxembourg Centre for Socio-Environmental Systems
Extrapolated empirical likelihood as a solution to the convex-hull-violation problem
Abstract
Empirical likelihood (EL) breaks down when the hypothesised mean falls outside the convex hull of the sample. We develop two splicing schemes, which we call extrapolated EL (ExEL), that extend the log-EL ratio beyond the convex hull while leaving it unchanged in a user-specified interior region. The first scheme, ExEL1, continues EL past a data-driven cut-off via its local quadratic (Taylor) expansion. The second scheme, ExEL2, smoothly splices EL to its global quadratic Wald approximation using 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 allows researchers to distinguish between mild and severe violations. Furthermore, it has nice inferential properties, yielding accurate coverage probabilities with bootstrap calibration.
Language
English
This is a free seminar. Registration is mandatory.