A goodness-of-fit test for single-index models

Yingcun XIA, Wai Keung LI, Howell TONG, Dixin ZHANG

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46 Citations (Scopus)


The single-index model with an unknown link function is a generalized linear model that has been intensively investigated. This article considers a goodness-of-fit test for this model. Cramér-von Mises tests are constructed and the bootstrap method is used to provide p- values. The problem of bias in nonparametric estimation is tackled by the bootstrap method. Therefore, we do not need to undersmooth or oversmooth the link function. Some simulations are reported and some data are used for illustration. Copyright © 2004 Institute of Statistical Science, Academia Sinica.
Original languageEnglish
Pages (from-to)1-28
JournalStatistica Sinica
Issue number1
Publication statusPublished - Jan 2004


Xia, Y., Li, W. K., Tong, H., & Zhang, D. (2004). A goodness-of-fit test for single-index models. Statistica Sinica, 14(1), 1-28.


  • Bias correction
  • Bootstrap
  • Cramér-von Mises test
  • Goodness of fit
  • Local linear smoother
  • Single-index model


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