A robust adaptive-to-model enhancement test for parametric single-index models

Cuizhen Niu, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


This paper is devoted to test the parametric single-index structure of the underlying model when there are outliers in observations. First, a test that is robust against outliers is suggested. The Hampel’s second-order influence function of the test statistic is proved to be bounded. Second, the test fully uses the dimension reduction structure of the hypothetical model and automatically adapts to alternative models when the null hypothesis is false. Thus, the test can greatly overcome the dimensionality problem and is still omnibus against general alternative models. The performance of the test is demonstrated by both Monte Carlo simulation studies and an application to a real dataset.

Original languageEnglish
Pages (from-to)1013-1045
Number of pages33
JournalAnnals of the Institute of Statistical Mathematics
Issue number5
Publication statusPublished - 1 Oct 2018

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Bounded influence function
  • Dimension reduction
  • Model checking
  • Omnibus property
  • Robust adaptive-to-model test


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