Efficient estimation for partially linear varying-coefficient errors-in-variables models with heteroscedastic errors

Efficient estimation for partially linear varying-coefficient errors-in-variables models with heteroscedastic errors

Hongxia XuXiaoming Duan 

Department of Mathematics, Shanghai Maritime University, Shanghai 201306, China

School of Economics and Management, Shanghai Maritime University, Shanghai 201306, China

Corresponding Author Email: 
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This paper studies the varying-coefficient heteroscedastic partially linear models where some covariates are measured with additive errors. To eliminate the bias of the usual profile least squares estimation when measurement errors are ignored, a modified profile least squares estimator of the regression parameter is suggested and the local polynomial smoother is applied to constructing estimators of the varying coefficient function and error variance function. Further, for the purpose of accounting for heteroscedasticity and the estimation accuracy, re-weighted estimations of the regression parameter and varying coefficient function are proposed. Asymptotic behaviors of the above estimators are established and the re-weighted estimator is shown to be more efficient than the modified profile least-squares estimator. Both simulated and real data examples are conducted to illustrate the applications of the proposed approaches.


varying-coefficient partially linear model, profile least squares, errors-in-variables, heteroscedasticity, re-weighted estimation

1. Introduction
2. Estimation methodology
3. Main results
4. Simulation study

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