Estimation in a semiparametric partially linear errors-in-variables model
Liang, Hua ; Härdle, Wolfgang ; Carroll, Raymond J.
Ann. Statist., Tome 27 (1999) no. 4, p. 1519-1535 / Harvested from Project Euclid
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We consider the partially linear model relating a response $Y$ to predictors ($X, T$) with mean function $X^{\top}\beta + g(T)$ when the $X$’s are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis leads to biased estimates of both the parameter $\beta$ and the function $g(\cdot)$ when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of $\beta$ is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.
Publié le : 1999-10-14
Classification:  Errors-in-variables,  measurement error,  nonparametric likelihood,  orthogonal regression,  partially linear model,  semiparametric models,  structural relations,  62J99,  62H12,  62E25,  62F10,  62H25,  62F10,  62F12,  60F05 
@article{1017939140,
     author = {Liang, Hua and H\"ardle, Wolfgang and Carroll, Raymond J.},
     title = {Estimation in a semiparametric partially linear
			 errors-in-variables model},
     journal = {Ann. Statist.},
     volume = {27},
     number = {4},
     year = {1999},
     pages = { 1519-1535},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1017939140}
}

Liang, Hua; Härdle, Wolfgang; Carroll, Raymond J. Estimation in a semiparametric partially linear
			 errors-in-variables model. Ann. Statist., Tome 27 (1999) no. 4, pp.  1519-1535. http://gdmltest.u-ga.fr/item/1017939140/