Optimal difference-based estimation for partially linear models

Yuejin Zhou, Yebin Cheng, Wenlin Dai, Tiejun Tong

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish (US)
Pages (from-to)863-885
Number of pages23
JournalComputational Statistics
Issue number2
StatePublished - Dec 16 2017


Dive into the research topics of 'Optimal difference-based estimation for partially linear models'. Together they form a unique fingerprint.

Cite this