Abstract
As a generalization of nonparametric regression model, partially linear model has been studied extensively in the last decades. This paper considers estimation of the semiparametric model under the situation that the covariates are measured with additive error in the linear part and some additional stochastic linear restrictions exist on the parametric component. Based on the corrected profile least-squares approach and mixed regression method, we propose a stochastic restricted estimator named the corrected profile mixed estimator for the parametric component, and discuss its statistical properties. We also construct a weighted stochastic restricted estimation for the parametric component. Finally, the proposed procedure is illustrated by simulation studies.
Highlights
In the last two decades, semiparametric measurement error models have received considerable attention in statistics and econometrics
This paper considers estimation of the semiparametric model under the situation that the covariates are measured with additive error in the linear part and some additional stochastic linear restrictions exist on the parametric component
Based on the corrected profile least-squares approach and mixed regression method, we propose a stochastic restricted estimator named the corrected profile mixed estimator for the parametric component, and discuss its statistical properties
Summary
In the last two decades, semiparametric measurement error (errors-in-variables) models have received considerable attention in statistics and econometrics. The following structural partially linear errors-in-variables model is considered. Measurement error models with exact or stochastic restrictions have been studied by many authors. For the linear measurement error models, Shalabh et al (2007) and Shalabh et al (2009) studied the exact restricted estimation. Shalabh et al (2010) and Li and Yang (2013) studied the estimation of the model when stochastic linear restrictions on regression coefficients are available. For the partially linear measurement error model with exact linear restrictions, Wei et al (2013) proposed a restricted corrected profile least-squares estimator for the parametric component.
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