Difference based estimation for partially linear regression models with measurement errors |
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Authors: | Haibing Zhao Jinhong You |
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Affiliation: | aSchool of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, PR China |
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Abstract: | This paper is concerned with the estimating problem of the partially linear regression models where the linear covariates are measured with additive errors. A difference based estimation is proposed to estimate the parametric component. We show that the resulting estimator is asymptotically unbiased and achieves the semiparametric efficiency bound if the order of the difference tends to infinity. The asymptotic normality of the resulting estimator is established as well. Compared with the corrected profile least squares estimation, the proposed procedure avoids the bandwidth selection. In addition, the difference based estimation of the error variance is also considered. For the nonparametric component, the local polynomial technique is implemented. The finite sample properties of the developed methodology is investigated through simulation studies. An example of application is also illustrated. |
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Keywords: | AMS subject classifications: 62G20 62G08 |
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