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Description:
We present results of a simulation study regarding the finite-sample type I error behavior of the self-concordant profile empirical likelihood ratio (ELR) test for the population correlation coefficient. Three different families of bivariate elliptical distributions are taken into account. Uniformly over all considered models and parameter configurations, the self-concordant profile ELR test does not keep the significance level for finite sample sizes, albeit the level exceedance monotonously decreases to zero as the sample size increases. We discuss some potential modifications to address this problem.