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Recently, a technique based on pseudo-observations has been proposed to tackle the so called convex hull problem for the empirical likelihood statistic. The resulting adjusted empirical likelihood also achieves the highorder precision of the Bartlett correction. Nevertheless, the technique induces an upper bound on the resulting statistic that may lead, in certain circumstances, to worthless confidence regions equal to the whole parameter space. In this paper we show that suitable pseudo-observations can be deployed to make each element of the generalised power divergence family Bartlett-correctable and released from the convex hull problem. Our approach is conceived to achieve this goal by means of two distinct sets of pseudo-observations with dfferent tasks. An important effect of our formulation is to provide a solution that permits to overcome the problem of the upper bound. The proposal, whose effectiveness is confirmed by simulation results, gives back attractiveness to a broad class of statistics that potentially contains good alternatives to the empirical likelihood.

The evaluation of the ability of a diagnostic test to separate diseaded from non-diseaded subjects is a crucial issue in modern medicine. The accuracy of a continuous-scale test, at a chosen cut-off level, can be measured by its sensitivity and specificity, i.e. by the probabilities that the test correctly identifies the diseaded and non-diseaded subjects, respectively. In practice, sensitivity and specificity of the test are unknown. Moreover, the cut-o level to use is also generally unknown, in that no preliminary indications driving its choice could be available. In this paper, we try to address the problem of making joint inference on pairs of quantities defining accuracy of a diagnostic test, in particular when one of the two quantities is the cut-off level. We propose a technique based on an empirical likelihood statistic that allows, within a unified framework, to make inference about the pair (sensitivity, cut-off level), at a fixed value of specificity, as well as about the pair (specificity, cut-off level), at a fixed value of sensitivity, or about the pair (sensitivity, specificity), at a fixed cut-off value. A simulation study is carried out to assess the finite-sample accuracy of the method. Moreover, we apply the method to two real examples.

Let X and Y be two independent continuous random variables. We discuss three techniques to obtain confidence intervals for ρ_Pr[Y > X] in a semiparametric framework. One method relies on the asymptotic normality of an estimator for ρ; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. An illustration is given using a dataset on the detection of carriers of Duchenne Muscular Dystrophy.

This paper presents a new quasi-profile loglikelihood with the standard kind of distributional limit behaviour, for inference about an arbitrary one-dimensional parameter of interest, based on unbiased estimating functions. The new function is obtained by requiring to the corresponding quasi-profile score function to have bias and information bias of order 0(1). We illustrate the use of the proposed pseudo-likelihood with an application for robust inference in linear models.