IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v68y2016i2p329-351.html
   My bibliography  Save this article

Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data

Author

Listed:
  • Ke-Hai Yuan
  • Wai Chan
  • Yubin Tian

Abstract

Means and covariance/dispersion matrix are the building blocks for many statistical analyses. By naturally extending the score functions based on a multivariate $$t$$ t -distribution to estimating equations, this article defines a class of M-estimators of means and dispersion matrix for samples with missing data. An expectation-robust (ER) algorithm solving the estimating equations is obtained. The obtained relationship between the ER algorithm and the corresponding estimating equations allows us to obtain consistent standard errors when robust means and dispersion matrix are further analyzed. Estimating equations corresponding to existing ER algorithms for computing M- and S-estimators are also identified. Monte Carlo results show that robust methods outperform the normal-distribution-based maximum likelihood when the population distribution has heavy tails or when data are contaminated. Applications of the results to robust analysis of linear regression and growth curve models are discussed. Copyright The Institute of Statistical Mathematics, Tokyo 2016

Suggested Citation

  • Ke-Hai Yuan & Wai Chan & Yubin Tian, 2016. "Expectation-robust algorithm and estimating equations for means and dispersion matrix with missing data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 329-351, April.
    • Handle: RePEc:spr:aistmt:v:68:y:2016:i:2:p:329-351
    DOI: 10.1007/s10463-014-0498-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-014-0498-1
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-014-0498-1?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Ke-Hai Yuan & Fan Yang-Wallentin & Peter M. Bentler, 2012. "ML Versus MI for Missing Data With Violation of Distribution Conditions," Sociological Methods & Research, , vol. 41(4), pages 598-629, November.
    2. Ke-Hai Yuan & Peter Bentler & Wai Chan, 2004. "Structural equation modeling with heavy tailed distributions," Psychometrika, Springer;The Psychometric Society, vol. 69(3), pages 421-436, September.
    3. Roderick J. A. Little, 1988. "Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 23-38, March.
    4. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
    5. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 803-826, October.
    6. Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hayakawa, Kazuhiko, 2024. "Recent development of covariance structure analysis in economics," Econometrics and Statistics, Elsevier, vol. 29(C), pages 31-48.
    2. Ke-Hai Yuan & Mortaza Jamshidian & Yutaka Kano, 2018. "Missing Data Mechanisms and Homogeneity of Means and Variances–Covariances," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 425-442, June.

    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. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 803-826, October.
    2. Yuan, Ke-Hai, 2009. "Normal distribution based pseudo ML for missing data: With applications to mean and covariance structure analysis," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1900-1918, October.
    3. Yuan, Ke-Hai & Savalei, Victoria, 2014. "Consistency, bias and efficiency of the normal-distribution-based MLE: The role of auxiliary variables," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 353-370.
    4. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    5. Tian, Guo-Liang & Ng, Kai Wang & Tan, Ming, 2008. "EM-type algorithms for computing restricted MLEs in multivariate normal distributions and multivariate t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4768-4778, June.
    6. Jie Jiang & Xinsheng Liu & Keming Yu, 2013. "Maximum likelihood estimation of multinomial probit factor analysis models for multivariate t-distribution," Computational Statistics, Springer, vol. 28(4), pages 1485-1500, August.
    7. R. M. Balan & Ioana Schiopu-Kratina, 2004. "Asymptotic Results with Generalized Estimating Equations for Longitudinal data II," RePAd Working Paper Series lrsp-TRS398, Département des sciences administratives, UQO.
    8. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    9. Jonathan Schweig, 2014. "Multilevel Factor Analysis by Model Segregation," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 394-422, October.
    10. Boik, Robert J., 2008. "An implicit function approach to constrained optimization with applications to asymptotic expansions," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 465-489, March.
    11. Kano, Yutaka & Takai, Keiji, 2011. "Analysis of NMAR missing data without specifying missing-data mechanisms in a linear latent variate model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1241-1255, October.
    12. Bosco, Bruno & Parisio, Lucia & Pelagatti, Matteo & Baldi, Fabio, 2007. "A Robust Multivariate Long Run Analysis of European Electricity Prices," International Energy Markets Working Papers 7438, Fondazione Eni Enrico Mattei (FEEM).
    13. Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
    14. Ke-Hai Yuan & Kentaro Hayashi, 2005. "On muthén’s maximum likelihood for two-level covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 147-167, March.
    15. 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.
    16. Feng, Jiarui & Zhu, Zhongyi, 2011. "Semiparametric analysis of longitudinal zero-inflated count data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 61-72, January.
    17. Frahm, Gabriel & Nordhausen, Klaus & Oja, Hannu, 2020. "M-estimation with incomplete and dependent multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    18. Taehun Lee & Li Cai, 2012. "Alternative Multiple Imputation Inference for Mean and Covariance Structure Modeling," Journal of Educational and Behavioral Statistics, , vol. 37(6), pages 675-702, December.
    19. V. Lachos & T. Angolini & C. Abanto-Valle, 2011. "On estimation and local influence analysis for measurement errors models under heavy-tailed distributions," Statistical Papers, Springer, vol. 52(3), pages 567-590, August.
    20. Claeskens, Gerda & Aerts, Marc, 2000. "On local estimating equations in additive multiparameter models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 139-148, August.

    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:aistmt:v:68:y:2016:i:2:p:329-351. 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.