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Abstract:
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Empirical likelihood is an important nonparametric statistical methodology. A package in R called "emplik," with main function "el.test," implements empirical likelihood for inference about a multivariate mean but sometimes gives a wrong empirical likelihood. We have written five other functions that seek to achieve the same goal as "el.test" and present comparison of their properties. These methods are Newton, Davidon-Fletcher-Powell (DFP), Broyden-Fletcher-Goldfarb-Shanno, conjugate gradient method, and damped Newton respectively. Theoretically, damped Newton and DFP are guaranteed to succeed. Practically, damped Newton is as fast as "el.test" and always gives the correct empirical likelihood. The function "el.test" differs a little from others. It performs badly because at almost every step it moved toward the steepest descent direction rather than the Newton direction.
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