Locally efficient estimation in generalized partially linear model with measurement error in nonlinear function
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We investigate the errors in covariates issues in a generalized partially linear model. Different from the usual literature (Ma and Carroll in J Am Stat Assoc 101:1465–1474, 2006), we consider the case where the measurement error occurs to the covariate that enters the model nonparametrically, while the covariates precisely observed enter the model parametrically. To avoid the deconvolution type operations, which can suffer from very low convergence rate, we use the B-splines representation to approximate the nonparametric function and convert the problem into a parametric form for operational purpose. We then use a parametric working model to replace the distribution of the unobservable variable, and devise an estimating equation to estimate both the model parameters and the functional dependence of the response on the latent variable. The estimation procedure is devised under the functional model framework without assuming any distribution structure of the latent variable. We further derive theories on the large sample properties of our estimator. Numerical simulation studies are carried out to evaluate the finite sample performance, and the practical performance of the method is illustrated through a data example.
KeywordsB-splines Efficient score Errors in variables Generalized linear models Instrumental variables Measurement errors Partially linear models Semiparametrics
Mathematics Subject Classification62F12 62J02 62J12
- Jiang F, Ma Y (2018) A spline-assisted semiparametric approach to nonparametric measurement error models. arXiv:1804.00793