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The Infinitesimal Jackknife and Analysis of Higher Order Moments

  • Robert JennrichEmail author
  • Albert Satorra
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 140)

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 (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.

Keywords

Kronecker Product Latent Variable Model High Order Moment Sample Covariance Matrix Factor Analysis Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bentler, P. M. (2012). EQS 6 structural equations program manual. Encino, CA: Multivariate Software.Google Scholar
  2. Cragg, J. G. (1997). Using higher order moments to estimate the simple errors-in-variables model. The Rand Journal of Economics, 28, Special Issue in honor of Richard E. Quandt, S71–S91.Google Scholar
  3. Efron, B., & Tibshirani, R. J. (1993). An introduction to the Bootstrap. New York: Chapman & Hall.CrossRefzbMATHGoogle Scholar
  4. Hausman, J. A., Newey, W. K., Ichimura, H., & Powell, J. L. (1991). Identification and estimation of polynomial errors-in-variables models. Journal of Econometrics, 50, 273–295.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Jaeckel, L. (1972). The infinitesimal jackknife. Memorandum #MM 72-1215-11. Murray Hill, NJ: Bell Laboratories.Google Scholar
  6. Jennrich, R. I. (2008). Nonparametric estimation of standard errors in covariance structure analysis. Psychometrika, 73, 579–594.MathSciNetCrossRefzbMATHGoogle Scholar
  7. Jennrich, R. I., & Satorra, A. (in press). The infinitesimal jackknife and moment structure analysis using higher order moments. Psychometrika.Google Scholar
  8. Mooijaart, A. (1985). Factor analysis of non-normal variables. Psychometrika, 50, 323–342.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Mooijaart, A., & Bentler, P. M. (2010). An alternative approach for non-linear latent variable models. Structural Equation Modeling, 17, 357–373.MathSciNetCrossRefGoogle Scholar
  10. Ozaki, K., Toyoda, H., Iwama, N., Kubo, S., & Ando, J. (2011). Using non-normal SEM to resolve the ACDE model in the classical twin design. Behavioral Genetics, 41, 329–339.CrossRefGoogle Scholar
  11. Pal, M. (1980). Consistent moment estimators of regression coefficients in the presence of errors in variables. Journal of Econometrics, 14, 349–364.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.Universitat Pompeu FabraBarcelonaSpain

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