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. 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.
    3. 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.
    4. 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.
    5. Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
    6. 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.
    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. 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.
    5. Wang, Xiao, 2010. "Wiener processes with random effects for degradation data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 340-351, February.
    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. Jean Jacod & Michael Sørensen, 2018. "A review of asymptotic theory of estimating functions," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 415-434, July.
    8. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    9. Ron Mittelhammer & George Judge, 2009. "A Minimum Power Divergence Class of CDFs and Estimators for the Binary Choice Model," International Econometric Review (IER), Econometric Research Association, vol. 1(1), pages 33-49, April.
    10. 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.
    11. Y. Fong & J. Wakefield & S. De Rosa & N. Frahm, 2012. "A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems," Biometrics, The International Biometric Society, vol. 68(4), pages 1103-1112, December.
    12. Frahm, Gabriel & Jaekel, Uwe, 2010. "A generalization of Tyler's M-estimators to the case of incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 374-393, February.
    13. 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.
    14. Kilic, Talip & Zezza, Alberto & Carletto, Calogero & Savastano, Sara, 2017. "Missing(ness) in Action: Selectivity Bias in GPS-Based Land Area Measurements," World Development, Elsevier, vol. 92(C), pages 143-157.
    15. Bello, A. L., 1995. "Imputation techniques in regression analysis: Looking closely at their implementation," Computational Statistics & Data Analysis, Elsevier, vol. 20(1), pages 45-57, July.
    16. Lingzhi Chen & Ričardas Zitikis, 2020. "Quantifying and analyzing nonlinear relationships with a fresh look at a classical dataset of student scores," Quality & Quantity: International Journal of Methodology, Springer, vol. 54(4), pages 1145-1169, August.
    17. Jonathan Schweig, 2014. "Multilevel Factor Analysis by Model Segregation," Journal of Educational and Behavioral Statistics, , vol. 39(5), pages 394-422, October.
    18. 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.
    19. Gregory Imholte & Raphael Gottardo, 2016. "Bayesian hierarchical modeling for subject‐level response classification in peptide microarray immunoassays," Biometrics, The International Biometric Society, vol. 72(4), pages 1206-1215, December.
    20. 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.

    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.