TY - JOUR
T1 - Optimal difference-based estimation for partially linear models
AU - Zhou, Yuejin
AU - Cheng, Yebin
AU - Dai, Wenlin
AU - Tong, Tiejun
N1 - Funding Information:
Acknowledgements 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).
PY - 2018/6/1
Y1 - 2018/6/1
N2 - 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.
AB - 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.
KW - Asymptotic normality
KW - Difference sequence
KW - Difference-based method
KW - Least squares estimator
KW - Partially linear model
UR - http://www.scopus.com/inward/record.url?scp=85038087246&partnerID=8YFLogxK
U2 - 10.1007/s00180-017-0786-3
DO - 10.1007/s00180-017-0786-3
M3 - Journal article
AN - SCOPUS:85038087246
SN - 0943-4062
VL - 33
SP - 863
EP - 885
JO - Computational Statistics
JF - Computational Statistics
IS - 2
ER -