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Asymptotics of Estimating Equations under Natural Conditions


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  • Yuan, Ke-Hai
  • Jennrich, Robert I.
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    In a variety of statistical problems one needs to solve an equation in order to get an estimator. We consider the large sample properties of such estimators generated from samples that are not necessarily identically distributed. Very general assumptions that lead to the existence, strong consistency, and asymptotic normality of the estimators are given. A number of results that are useful in verifying the general assumptions are given and an example illustrates their use. General applications to maximum likelihood, iteratively reweighted least squares, and robust estimation are discussed briefly.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 65 (1998)
    Issue (Month): 2 (May)
    Pages: 245-260

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    Handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:245-260

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    Keywords: Consistent solution; asymptotic normality; multivariate data; nonidentically distributed data; maximum likelihood; iteratively reweighted least squares; robust estimation;


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    1. Cheng, Ching-Shui & Li, Ker-Chau, 1984. "The strong consistency of M-estimators in linear models," Journal of Multivariate Analysis, Elsevier, vol. 15(1), pages 91-98, August.
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    Cited by:
    1. Tsimikas, John V. & Bantis, Leonidas E. & Georgiou, Stelios D., 2012. "Inference in generalized linear regression models with a censored covariate," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1854-1868.
    2. Ke-Hai Yuan & Brad Bushman, 2002. "Combining standardized mean differences using the method of maximum likelihood," Psychometrika, Springer, vol. 67(4), pages 589-607, December.
    3. 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.
    4. Claeskens, Gerda & Aerts, Marc, 2000. "On local estimating equations in additive multiparameter models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 139-148, August.
    5. Ke-Hai Yuan & Kentaro Hayashi, 2005. "On muthén’s maximum likelihood for two-level covariance structure models," Psychometrika, Springer, vol. 70(1), pages 147-167, March.
    6. Mittelhammer, Ronald C. & Judge, George G, 2008. "A minimum power divergence class of CDFs and estimators for binary choice models," CUDARE Working Paper Series 1059, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
    7. Yuan, Ke-Hai & Bentler, Peter M., 2006. "Asymptotic robustness of standard errors in multilevel structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1121-1141, May.
    8. 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.
    9. Susana Rubin-Bleuer & Ioana Schiopu Kratina, 2001. "On the two-phase framework for joint model and design-based inference," RePAd Working Paper Series lrsp-TRS382, Département des sciences administratives, UQO.
    10. Ke-Hai Yuan & Zhiyong Zhang, 2012. "Robust Structural Equation Modeling with Missing Data and Auxiliary Variables," Psychometrika, Springer, vol. 77(4), pages 803-826, October.
    11. Yuan, Ke-Hai & Bentler, Peter M., 2003. "Eight test statistics for multilevel structural equation models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 89-107, October.
    12. 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.
    13. 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.
    14. 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.


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