On the Estimation of Kurtosis Parameter in Elliptical Distributions

This paper discusses estimation of the kurtosis parameter, a key parameter in elliptical distributions. Asymptotic properties of the usual consistent estimator of kurtosis parameter in elliptical distributions are given by the perturbation method. Estimators with bias correction based on an asymptotic expansion of the expectation of the usual estimator are also given. Finally, the bias and the mean square error for the estimators are investigated by Monte Carlo simulation for some selected parameters.