The asymptotic kurtosis for maximum likelihood estimators

In general, when moments exist, the dominant term in the fourth central moment of an estimator is three times the square of the asymptotic variance: this to the value three for the asymptotic kurtosis. Working on the approach given in Bowman and Shenton (1998) we now complete the basic asymptotic moment profile by giving an expression for the third order term in the fourth central monment of maximum likelihood estimator, assuming the existence of derivatives of n density and also the existence of the covariance matrix inverse. A four moment distributional model, such as the Pearson system, or Johnson translation system, may be used to approximate pcrccntage points of the estimators.