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Asymptotics of Estimating Equations under Natural Conditions

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  • Yuan, Ke-Hai
  • Jennrich, Robert I.

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:245-260
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    References listed on IDEAS

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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. David Magis, 2016. "Efficient Standard Error Formulas of Ability Estimators with Dichotomous Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 184-200, March.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Mittelhammer, Ron C Dr. & Judge, George G., 2008. "A Minimum Power Divergence Class of CDFs and Estimators for Binary Choice Models," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7bc2828q, Department of Agricultural & Resource Economics, UC Berkeley.
    8. 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.
    9. Rubin-Bleuer, Susana, 2011. "The proportional hazards model for survey data from independent and clustered super-populations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 884-895, May.
    10. Niu, Yi & Peng, Yingwei, 2015. "A new estimating equation approach for marginal hazard ratio estimation," Computational Statistics & Data Analysis, Elsevier, vol. 87(C), pages 46-56.
    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. 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.
    13. 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.
    14. Guo You Qin & Zhong Yi Zhu, 2009. "Robustified Maximum Likelihood Estimation in Generalized Partial Linear Mixed Model for Longitudinal Data," Biometrics, The International Biometric Society, vol. 65(1), pages 52-59, March.
    15. Claeskens, Gerda & Aerts, Marc, 2000. "On local estimating equations in additive multiparameter models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 139-148, August.
    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. Ke-Hai Yuan & Brad Bushman, 2002. "Combining standardized mean differences using the method of maximum likelihood," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 589-607, December.
    18. 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.
    19. 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.
    20. Kuchibhotla, Arun Kumar & Basu, Ayanendranath, 2015. "A general set up for minimum disparity estimation," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 68-74.

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