Modern likelihood inference for the parameter of skewness: An application to mono-zygotic twin studies

We consider the use of modern likelihood asymptotics in the construction of confidence intervals for the parameter which determines the skewness of the distribution of the maximum/minimum of an exchangeable bivariate normal random vector. This distribution represents the reference model for assessing the degree of concordance of a continuos mono-zygotic twin trait when interest focuses on the pairwise maximum or minimum. Simulation studies were conducted to investigate the accuracy of the proposed method and to compare it to available alternatives. Accuracy is evaluated in terms of both coverage probability and expected length of the interval. We, furthermore, illustrate the suitability of our method by re-analyzing the data from a study which compares different measurements taken on the brains of mono-zygotic twins.