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Sieve empirical likelihood ratio tests for nonparametric functions

Jianqing Fan Jian Zhang

Statistics Theory and Methods mathscidoc:1912.43316

The Annals of Statistics, 32, (5), 1858-1907, 2004
Generalized likelihood ratio statistics have been proposed in Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153193] as a generally applicable method for testing nonparametric hypotheses about nonparametric functions. The likelihood ratio statistics are constructed based on the assumption that the distributions of stochastic errors are in a certain parametric family. We extend their work to the case where the error distribution is completely unspecified via newly proposed sieve empirical likelihood ratio (SELR) tests. The approach is also applied to test conditional estimating equations on the distributions of stochastic errors. It is shown that the proposed SELR statistics follow asymptotically rescaled 2-distributions, with the scale constants and the degrees of freedom being independent of the nuisance parameters. This demonstrates that the Wilks phenomenon observed in Fan, Zhang and Zhang [Ann. Statist. 29
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@inproceedings{jianqing2004sieve,
  title={Sieve empirical likelihood ratio tests for nonparametric functions},
  author={Jianqing Fan, and Jian Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113653372408876},
  booktitle={The Annals of Statistics},
  volume={32},
  number={5},
  pages={1858-1907},
  year={2004},
}
Jianqing Fan, and Jian Zhang. Sieve empirical likelihood ratio tests for nonparametric functions. 2004. Vol. 32. In The Annals of Statistics. pp.1858-1907. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113653372408876.
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