Geodesic
Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters
Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 69-81

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We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector $\theta$ to be estimated that also appears in the distribution of the regressor variable $x.$ The estimation of $\theta$ is based on an extended quasi score $(QS)$ function. Of special interest is the case where the distribution of $x$ depends only on a subvector $\alpha$ of $\theta,$ which may be considered a nuisance parameter. A major application of this model is the classical measurement error model, where the corrected score $(CS)$ estimator is an alternative to the $QS$ estimator. Under unknown nuisance parameters we derive conditions under which the $QS$ estimator is strictly more efficient than the $CS$ estimator. We focus on the loglinear Poisson, the Gamma, and the logit model.
Keywords: Mean-variance model, measurement error model, quasi score estimator, corrected score estimator, nuisance parameter, optimality property. 
@article{THSP_2007_13_4_a4,
     author = {Alexander Kukush and Andrii Malenko and Hans Schneeweiss},
     title = {Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {69--81},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a4/}
}
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Alexander Kukush; Andrii Malenko; Hans Schneeweiss. Comparing the efficiency of estimates in concrete errors-in-variables models under unknown nuisance parameters. Teoriâ slučajnyh processov, Tome 13 (2007) no. 4, pp. 69-81. http://geodesic.mathdoc.fr/item/THSP_2007_13_4_a4/