title: The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments.
abstract: 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 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 infinitesimal jackknife is the ease with which it may be used when stacking or sub-setting estimators. The estimates given are used to test the goodness of fit of a non-linear factor analysis model. A computationally accelerated form for infinitesimal jackknife estimates is given.
authors.affiliation: University Of California Los Angeles, 3400 Purdue Ave., Los Angeles, CA, 90066, USA. rij@stat.ucla.edu.
authors.forename: Robert
authors.initials: R
authors.lastname: Jennrich
authors.affiliation: Universitat Pompeu Fabra, Barcelona, Spain.
authors.forename: Albert
authors.initials: A
authors.lastname: Satorra
mesh_terms: D000465:Algorithms; D015982:Bias; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011594:Psychometrics
keywords: Acceleration; Asymptotically normal; Goodness of fit; Influence functions; Kronecker products; Pseudo-values