IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v81y2016i1p90-101.html

The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments

Author

Listed:
  • Robert Jennrich

  • Albert Satorra

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. Copyright The Psychometric Society 2016

Suggested Citation

  • Robert Jennrich & Albert Satorra, 2016. "The Infinitesimal Jackknife and Moment Structure Analysis Using Higher Order Moments," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 90-101, March.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:1:p:90-101
    DOI: 10.1007/s11336-014-9426-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-014-9426-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-014-9426-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Robert Jennrich & Albert Satorra, 2013. "Erratum to: Continuous orthogonal complement functions and distribution-free goodness of fit tests in moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 553-553, July.
    2. Robert Jennrich & Albert Satorra, 2013. "Continuous Orthogonal Complement Functions and Distribution-Free Goodness of Fit Tests in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 545-552, July.
    3. Ab Mooijaart, 1985. "Factor analysis for non-normal variables," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 323-342, September.
    4. Robert Jennrich, 2008. "Nonparametric Estimation of Standard Errors in Covariance Analysis Using the Infinitesimal Jackknife," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 579-594, December.
    5. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Albert Satorra & Heinz Neudecker, 2015. "A Theorem on the Rank of a Product of Matrices with Illustration of Its Use in Goodness of Fit Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 938-948, December.
    2. Lifang Deng & Ke-Hai Yuan, 2016. "Comparing Latent Means Without Mean Structure Models: A Projection-Based Approach," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 802-829, September.
    3. Michael Browne & Alexander Shapiro, 2015. "Comment on the Asymptotics of a Distribution-Free Goodness of Fit Test Statistic," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 196-199, March.
    4. Sule Alan & Orazio Attanasio & Martin Browning, 2009. "Estimating Euler equations with noisy data: two exact GMM estimators," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(2), pages 309-324, March.
    5. Daniel Miles & Andrés Pereyra & Máximo Rossi, 2002. "The consistent estimation of income elasticity of environmental amenities in Uruguay," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 17(1), pages 67-89.
    6. Christoph Breunig & Stephan Martin, 2020. "Nonclassical Measurement Error in the Outcome Variable," Papers 2009.12665, arXiv.org, revised May 2021.
    7. Lance Lochner & Youngki Shin, 2014. "Understanding Earnings Dynamics: Identifying and Estimating the Changing Roles of Unobserved Ability, Permanent and Transitory Shocks," NBER Working Papers 20068, National Bureau of Economic Research, Inc.
    8. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    9. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information," Boston College Working Papers in Economics 676, Boston College Department of Economics.
    10. Laurence C. Baker, 1995. "HMOs and Fee-For-Service Health Care Expenditures: Evidence from Medicare," NBER Working Papers 5360, National Bureau of Economic Research, Inc.
    11. Zapata, Hector O. & Sulgham, Anil K., 2006. "A Semiparametric Approach to Estimate Engel curves using the US Micro Data," 2006 Annual meeting, July 23-26, Long Beach, CA 21092, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    12. Tey, (John) Yeong-Sheng & Shamsudin, Mad Nasir & Mohamed, Zainalabidin & Abdullah, Amin Mahir & Radam, Alias, 2009. "Evidence of Engel curves in food away from home: A study of Malaysia," MPRA Paper 14833, University Library of Munich, Germany.
    13. Ben-Moshe, Dan & D’Haultfœuille, Xavier & Lewbel, Arthur, 2017. "Identification of additive and polynomial models of mismeasured regressors without instruments," Journal of Econometrics, Elsevier, vol. 200(2), pages 207-222.
    14. Esteban M. Aucejo & Patrick Coate & Jane Cooley Fruehwirth & Sean Kelly & Zachary Mozenter, 2018. "Teacher effectiveness and classroom composition," CEP Discussion Papers dp1574, Centre for Economic Performance, LSE.
    15. Shrabani Mukherjee & Subhadri Sankar Mallik & Debdulal Thakur, 2019. "Tracking Financial Inclusion in India: A Study of SHG Initiatives," Indian Journal of Human Development, , vol. 13(1), pages 32-46, April.
    16. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    17. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
    18. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    19. Raymond Carroll & Xiaohong Chen & Yingyao Hu, 2010. "Identification and estimation of nonlinear models using two samples with nonclassical measurement errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 419-423.
    20. Moschini, GianCarlo, 2001. "Production risk and the estimation of ex-ante cost functions," Journal of Econometrics, Elsevier, vol. 100(2), pages 357-380, February.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:81:y:2016:i:1:p:90-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.