Nonparametric inference with generalized likelihood ratio tests

Jianqing Fan, Jiancheng Jiang

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


The advance of technology facilitates the collection of statistical data. Flexible and refined statistical models are widely sought in a large array of statistical problems. The question arises frequently whether or not a family of parametric or nonparametric models fit adequately the given data. In this paper we give a selective overview on nonparametric inferences using generalized likelihood ratio (GLR) statistics. We introduce generalized likelihood ratio statistics to test various null hypotheses against nonparametric alternatives. The trade-off between the flexibility of alternative models and the power of the statistical tests is emphasized. Well-established Wilks' phenomena are discussed for a variety of semi- and non-parametric models, which sheds light on other research using GLR tests. A number of open topics worthy of further study are given in a discussion section.

Original languageEnglish (US)
Pages (from-to)409-444
Number of pages36
Issue number3
StatePublished - Dec 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Asymptotic null distribution
  • Bootstrap
  • Generalized likelihood ratio
  • Nonparametric test
  • Power function
  • Wilks' phenomenon


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