Nonconcave penalized likelihood with a diverging number of parameters

Jianqing Fan Heng Peng

Statistics Theory and Methods mathscidoc:1912.43252

The Annals of Statistics, 32, (3), 928-961, 2004
A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of procedures has an oracle property when the number of parameters is finite. However, in most model selection problems the number of parameters should be large and grow with the sample size. In this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to as the sample size increases. Under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators. Furthermore, the consistency of the sandwich formula of the covariance matrix is demonstrated. Nonconcave penalized likelihood ratio statistics are discussed, and their
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  title={Nonconcave penalized likelihood with a diverging number of parameters},
  author={Jianqing Fan, and Heng Peng},
  booktitle={The Annals of Statistics},
Jianqing Fan, and Heng Peng. Nonconcave penalized likelihood with a diverging number of parameters. 2004. Vol. 32. In The Annals of Statistics. pp.928-961.
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