Optimal difference-based estimation for partially linear models

Yuejin Zhou*, Yebin Cheng, Wenlin Dai, Tiejun TONG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)863-885
Number of pages23
JournalComputational Statistics
Volume33
Issue number2
DOIs
Publication statusPublished - 1 Jun 2018

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Mathematics

User-Defined Keywords

  • Asymptotic normality
  • Difference sequence
  • Difference-based method
  • Least squares estimator
  • Partially linear model

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