The Infinitesimal Jackknife and Analysis of Higher Order Moments

Mean corrected higher order sample moments are asymptotically normally distributed. It is shown that both in the literature and popular software the estimates of their asymptotic covariance matrices are incorrect. An introduction to the infinitesimal jackknife (IJK) is given and it is shown how to use it to correctly estimate the asymptotic covariance matrices of higher order sample moments. Another advantage in using the IJK is the ease with which it may be used when stacking or subsetting estimators. The estimates given are used to test the goodness of fit of a nonlinear factor analysis model. A computationally accelerated form for IJK estimates is given.