Abstract
In a variety of statistical problems the estimate Θn of a parameter Θ is defined as the root of a generalized estimating equation Gn(Θnγn)=0 where γn is an estimate of a nuisance parameter γ. We give sufficient conditions for the asymptotic normality of #x0398;n defined in this way and derive their asymptotic distribution. A circumstance under which the asymptotic distribution of #x0398;n will not be influenced by that of γn) is noted. As an example, we consider a covariance structure analysis in which both the population mean and the population fourth-order moment are nuisance parameters. Applications to pseudo maximum likelihood, generalized least squares with estimated weights, and M-estimation with an estimated scale parameter are discussed briefly.
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Yuan, KH., Jennrich, R.I. Estimating Equations with Nuisance Parameters: Theory and Applications. Annals of the Institute of Statistical Mathematics 52, 343–350 (2000). https://doi.org/10.1023/A:1004122007440
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DOI: https://doi.org/10.1023/A:1004122007440