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Nonparametric inference with generalized likelihood ratio tests

Jianqing Fan Jiancheng Jiang

Statistics Theory and Methods mathscidoc:1912.43304

Test, 16, (3), 409-444, 2007.12
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 (<i>GLR</i>) 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 <i>GLR</i> tests. Anumber of open topics worthy of further study are given in a discussion section.
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@inproceedings{jianqing2007nonparametric,
  title={Nonparametric inference with generalized likelihood ratio tests},
  author={Jianqing Fan, and Jiancheng Jiang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113608883245864},
  booktitle={Test},
  volume={16},
  number={3},
  pages={409-444},
  year={2007},
}
Jianqing Fan, and Jiancheng Jiang. Nonparametric inference with generalized likelihood ratio tests. 2007. Vol. 16. In Test. pp.409-444. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113608883245864.
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