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Modified estimating functions

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  • Thomas A. Severini

Abstract

In a parametric model the maximum likelihood estimator of a parameter of interest &psgr; may be viewed as the solution to the equation l′-sub-p(&psgr;) = 0, where l-sub-p denotes the profile loglikelihood function. It is well known that the estimating function l′-sub-p(&psgr;) is not unbiased and that this bias can, in some cases, lead to poor estimates of &psgr;. An alternative approach is to use the modified profile likelihood function, or an approximation to the modified profile likelihood function, which yields an estimating function that is approximately unbiased. In many cases, the maximum likelihood estimating functions are unbiased under more general assumptions than those used to construct the likelihood function, for example under first- or second-moment conditions. Although the likelihood function itself may provide valid estimates under moment conditions alone, the modified profile likelihood requires a full parametric model. In this paper, modifications to l′-sub-p(&psgr;) are presented that yield an approximately unbiased estimating function under more general conditions. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • Thomas A. Severini, 2002. "Modified estimating functions," Biometrika, Biometrika Trust, vol. 89(2), pages 333-343, June.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:333-343
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    Cited by:

    1. Stefano Cabras & María Castellanos & Erlis Ruli, 2014. "A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 153-167, August.
    2. Hanfelt, John J. & Li, Ruosha & Pan, Yi & Payment, Pierre, 2011. "Robust inference for sparse cluster-correlated count data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 182-192, January.
    3. F. Bartolucci & R. Bellio & A. Salvan & N. Sartori, 2016. "Modified Profile Likelihood for Fixed-Effects Panel Data Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(7), pages 1271-1289, August.
    4. Manuel Arellano & Jinyong Hahn, 2005. "Understanding Bias in Nonlinear Panel Models: Some Recent Developments," Working Papers wp2005_0507, CEMFI.
    5. Lu Lin & Lixing Zhu & K. Yuen, 2005. "Profile empirical likelihood for parametric and semiparametric models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 485-505, September.

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