Jackknife empirical likelihood ratio test for testing the equality of semivariance

Semivariance is a measure of the dispersion of all observations that fall above the mean or target value of a random variable and it plays an important role in life-length, actuarial and income studies. In this paper, we develop a new non-parametric test for testing the equality of upper semivariance. We use the U-statistic theory to derive the test statistic and then study the asymptotic properties of the test statistic. We also develop a jackknife empirical likelihood (JEL) ratio test for testing the equality of upper semivariance. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed JEL-based test. We illustrate the test procedure using real data.