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    Optimal difference-based estimation for partially linear models

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    Type
    Article
    Authors
    Zhou, Yuejin cc
    Cheng, Yebin
    Dai, Wenlin
    Tong, Tiejun
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-12-16
    Permanent link to this record
    http://hdl.handle.net/10754/626605
    
    Metadata
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    Abstract
    Difference-based methods have attracted increasing attention for analyzing partially linear models in the recent literature. In this paper, we first propose to solve the optimal sequence selection problem in difference-based estimation for the linear component. To achieve the goal, a family of new sequences and a cross-validation method for selecting the adaptive sequence are proposed. We demonstrate that the existing sequences are only extreme cases in the proposed family. Secondly, we propose a new estimator for the residual variance by fitting a linear regression method to some difference-based estimators. Our proposed estimator achieves the asymptotic optimal rate of mean squared error. Simulation studies also demonstrate that our proposed estimator performs better than the existing estimator, especially when the sample size is small and the nonparametric function is rough.
    Citation
    Zhou Y, Cheng Y, Dai W, Tong T (2017) Optimal difference-based estimation for partially linear models. Computational Statistics. Available: http://dx.doi.org/10.1007/s00180-017-0786-3.
    Sponsors
    Yuejin Zhou’s research was supported in part by the Natural Science Foundation of Anhui Grant (No. KJ2017A087), and the National Natural Science Foundation of China Grant (No. 61472003). Yebin Cheng’s research was supported in part by the National Natural Science Foundation of China Grant (No. 11271241). Tiejun Tong’s research was supported in part by the Hong Kong Baptist University Grants FRG1/16-17/018 and FRG2/16-17/074, and the National Natural Science Foundation of China Grant (No. 11671338).
    Publisher
    Springer Nature
    Journal
    Computational Statistics
    DOI
    10.1007/s00180-017-0786-3
    Additional Links
    https://link.springer.com/article/10.1007%2Fs00180-017-0786-3
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00180-017-0786-3
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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