Semiparametric estimation of the single-index varying-coefficient model |
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Authors: | Yang Zhao Liugen Xue Sanying Feng |
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Affiliation: | 1. College of Applied Sciences, Beijing University of Technology, Beijing, China;2. Department of Mathematics, Nanchang University, Nanchang, China |
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Abstract: | In this paper, we consider the choice of pilot estimators for the single-index varying-coefficient model, which may result in radically different estimators, and develop the method for estimating the unknown parameter in this model. To estimate the unknown parameters efficiently, we use the outer product of gradient method to find the consistent initial estimators for interest parameters, and then adopt the refined estimation method to improve the efficiency, which is similar to the refined minimum average variance estimation method. An algorithm is proposed to estimate the model directly. Asymptotic properties for the proposed estimation procedure have been established. The bandwidth selection problem is also considered. Simulation studies are carried out to assess the finite sample performance of the proposed estimators, and efficiency comparisons between the estimation methods are made. |
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Keywords: | Asymptotic normality convergence of algorithm global cost function local linear smoothing single-index varying-coefficient model |
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