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 equality of upper semi-variance. 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 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.

翻译：半方差是衡量随机变量高于均值或目标值的所有观测值离散程度的一种度量，在寿命分析、精算学及收入研究中具有重要作用。本文提出了一种用于检验上半方差相等性的新非参数检验方法。我们利用U统计量理论推导出检验统计量，并研究了该统计量的渐近性质。同时，我们建立了基于刀切经验似然（JEL）的比率检验来检验上半方差的相等性。通过大量蒙特卡洛模拟研究验证了所提出的JEL检验的性能，并利用实际数据对检验过程进行了演示。