Simultaneous confidence bands and hypothesis testing for single-index models

Gaorong Li, Heng PENG, Kai Dong, Tiejun TONG

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

In this paper, we propose simultaneous confidence bands for the nonparametric link function in single-index models in the presence of a nuisance index parameter. We establish the asymptotic properties for the link function and its derivative that allow simultaneous confidence bands for various inference tasks. In addition, we propose an adaptive Neyman test statistic for testing the linearity of the link function. We then conduct simulation studies to evaluate the performance of the proposed method, and apply them to two data sets for illustration.

Original languageEnglish
Pages (from-to)937-955
Number of pages19
JournalStatistica Sinica
Volume24
Issue number2
DOIs
Publication statusPublished - 1 Apr 2014

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Adaptive Neyman test
  • Difference-based estimator
  • Local linear smoother
  • Residual variance
  • Simultaneous confidence band
  • Single-index model

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