Abstract: | Abstract. Suppose that X 1 ,…, X n is a sequence of independent random vectors, identically distributed as a d -dimensional random vector X . Let be a parameter of interest and be some nuisance parameter. The unknown, true parameters ( μ 0 , ν 0 ) are uniquely determined by the system of equations E { g ( X , μ 0 , ν 0 )} = 0 , where g = ( g 1 ,…, g p + q ) is a vector of p + q functions. In this paper we develop an empirical likelihood (EL) method to do inference for the parameter μ 0 . The results in this paper are valid under very mild conditions on the vector of criterion functions g . In particular, we do not require that g 1 ,…, g p + q are smooth in μ or ν . This offers the advantage that the criterion function may involve indicators, which are encountered when considering, e.g. differences of quantiles, copulas, ROC curves, to mention just a few examples. We prove the asymptotic limit of the empirical log-likelihood ratio, and carry out a small simulation study to test the performance of the proposed EL method for small samples. |