Optimal difference-based estimation for partially linear models
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 s...
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| Veröffentlicht in: | Computational statistics 2018-06, Vol.33 (2), p.863-885 |
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| creator | Zhou, Yuejin Cheng, Yebin Dai, Wenlin Tong, Tiejun |
| description | 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. |
| doi_str_mv | 10.1007/s00180-017-0786-3 |
| format | Article |
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| subjects | Asymptotic methods Computer simulation Economic Theory/Quantitative Economics/Mathematical Methods Error analysis Estimating techniques Mathematics and Statistics Original Paper Probability and Statistics in Computer Science Probability Theory and Stochastic Processes Regression analysis Statistics |
| title | Optimal difference-based estimation for partially linear models |
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