Small-sample likelihood asymptotics for the equi-correlated bivariate normal model

We discuss two likelihood-based small-sample confidence intervals for the skewness parameter of the distribution of the maximum (or minimum) of the equi-correlated bivariate normal model. These are compared numerically to their large-sample counterpart, and to an approximate confidence interval whose con- struction derives from theoretical findings on the intraclass correlation coefficient and Fisher’s transformation. The performance of the confidence intervals is analyzed in terms of actual coverage, symmetry of errors, and expected length. A simulation revealed that the considered small-sample procedures perform well even when the sample size is limited. A real-life application to a mono-zygotic twin study is also given.