Testing discontinuities in nonparametric regression

Wenlin Dai, Yuejin Zhou, Tiejun TONG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In nonparametric regression, it is often needed to detect whether there are jump discontinuities in the mean function. In this paper, we revisit the difference-based method in [13] and propose to further improve it. To achieve the goal, we first reveal that their method is less efficient due to the inappropriate choice of the response variable in their linear regression model. We then propose a new regression model for estimating the residual variance and the total amount of discontinuities simultaneously. In both theory and simulation, we show that the proposed variance estimator has a smaller mean-squared error compared to the existing estimator, whereas the estimation efficiency for the total amount of discontinuities remains unchanged. Finally, we construct a new test procedure for detection of discontinuities using the proposed method; and via simulation studies, we demonstrate that our new test procedure outperforms the existing one in most settings.

Original languageEnglish
Pages (from-to)450-473
Number of pages24
JournalJournal of Applied Statistics
Volume45
Issue number3
DOIs
Publication statusPublished - 17 Feb 2018

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Asymptotic normality
  • difference-based estimator
  • jump point
  • model selection
  • nonparametric regression
  • residual variance

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