Nonconcave penalized likelihood with a diverging number of parameters
Nonconcave penalized likelihood with a diverging number of parameters
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DOI：
10.1214/009053604000000256
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发表时间：
2004-06-01
影响因子：
4.5
通讯作者：
Peng, H
中科院分区：
文献类型：
--
作者：
Fan, JQ;Peng, H
Fan和Li提出了一类基于非凹惩罚似然的参数模型的变量选择方法，可同时估计参数和选择重要变量.他们证明了当参数的数量是有限的时，这类过程具有预言属性。然而，在大多数模型选择问题中，参数的数量应该很大，并随着样本量的增加而增加。本文针对参数数量随着样本量的增加而趋于无穷大的情况，建立了非凹惩罚似然的一些渐进性质。在正则性条件下，我们建立了惩罚似然估计的预言性质和渐近正态性。进一步证明了协方差矩阵夹心公式的一致性。讨论了非凹罚似然比统计量，通过对罚函数施加一些适当的条件，得到了它们在原假设下的渐近分布。渐近的结果增加了一个模拟研究，并说明了新开发的方法分析的法院案件的性别歧视的工资。
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 infinity 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 asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions. The asymptotic results are augmented by a simulation Study, and the newly developed methodology is illustrated by an analysis of a court case on the sexual discrimination of salary.