Jackknife empirical likelihood for the skewness and kurtosis

Coefficients of skewness and kurtosis provide convenient measures for describing the shape of a distribution based on a sample of independent observations. In this paper, we propose jackknife empirical likelihood (JEL) confidence intervals for the skewness and kurtosis coefficients, proving that the limiting distribution of the JEL ratio is a standard chi-squared distribution, and conduct an extensive simulation study comparing JEL with bootstrap methods. Compared with bootstrap methods, the JEL-based confidence intervals perform well in simulations with data from normal, t, gamma, log-normal, and uniform distributions. We also illustrate the application of our proposed JEL methods using data from the behavioral risk factor surveillance system, an annual US health survey.