Optimal difference-based estimation for partially linear models

Yuejin Zhou (), Yebin Cheng (), Wenlin Dai () and Tiejun Tong ()
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Yuejin Zhou: Anhui University of Science and Technology
Yebin Cheng: Donghua University
Wenlin Dai: King Abdullah University of Science and Technology
Tiejun Tong: Hong Kong Baptist University

Computational Statistics, 2018, vol. 33, issue 2, No 13, 863-885

Abstract: 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.

Keywords: Asymptotic normality; Difference-based method; Difference sequence; Least squares estimator; Partially linear model (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00180-017-0786-3

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