Estimation on semivarying coefficient models with different degrees of smoothness |
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Authors: | Riquan Zhang Jingyan Feng Kaichun Wen Jianhua Ding |
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Institution: | (1) Department of Statistics, East China Normal University, Shanghai, 200241, China;(2) Department of Mathematics, Shanxi Datong University, Datong, 037009, China;(3) Dagang No. 1 Middle School of Tianjin, Tianjin, 300270, China |
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Abstract: | Semivarying coefficient models are frequently used in statistical models. In this paper, under the condition that the coefficient
functions possess different degrees of smoothness, a two-step method is proposed. In the case, one-step method for the smoother
coefficient functions cannot be optimal. This drawback can be repaired by using the two-step estimation procedure. The asymptotic
mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation
studies are conducted to evaluate the proposed estimation methods.
This research is supported in part by the National Natural Science Foundation of China under Grant No. 10871072 and Shanxi's
Natural Science Foundation of China under Grant No. 2007011014. |
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Keywords: | Local polynomial regression one-step estimation optimal rate of convergence semi-varying coefficient model two-step estimation |
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