Estimation for varying coefficient partially nonlinear models with distorted measurement errors |
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Authors: | Shuang Dai Zhensheng Huang |
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Affiliation: | School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, PR China |
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Abstract: | In this paper, we propose a new varying coefficient partially nonlinear model where both the response and predictors are not directly observed, but are observed by unknown distorting functions of a commonly observable covariate. Because of the complexity of the model, existing estimation methods cannot be directly employed. For this, we propose using an efficient nonparametric regression to estimate the unknown distortion functions concerning the covariates and response on the distorting variable, and further, we obtain the profile nonlinear least squares estimators for the parameters and the coefficient functions using the calibrated variables. Furthermore, we establish the asymptotic properties of the resulting estimators. To illustrate our proposed methodology, we carry out some simulated and real examples. |
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Keywords: | primary 62G05 secondary 62G20 Distortion function Measurement error Profile nonlinear least-square method Varying coefficient partially nonlinear model |
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