Tuning parameter selection for penalised empirical likelihood with a diverging number of parameters
Tuning parameter selection for penalised empirical likelihood with a diverging number of parameters
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DOI：
10.1080/10485252.2020.1717491
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发表时间：
2020-01
影响因子：
1.2
通讯作者：
Chaowen Zheng;Yichao Wu
中科院分区：
文献类型：
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作者：
Chaowen Zheng;Yichao Wu
摘要惩罚似然法在分析高维数据方面取得了成功。Tang and Leng [（2010），'Penalized High-Dimensional Empirical Likelihood'，Biometrika，97（4），905-920]将惩罚方法扩展到经验似然情景，并表明惩罚经验似然估计量可以在线性回归模型中一致地识别真正的预测因子。然而，这种所需的选择一致性属性的惩罚经验似然方法在很大程度上依赖于调谐参数的选择。在这项工作中，我们提出了一个调整参数的选择过程，惩罚经验似然，以保证这种选择的一致性可以实现。具体来说，我们提出了一个广义信息准则（GIC）的惩罚经验似然线性回归的情况下。我们表明，调整参数选择的GIC产生真正的模型一致，即使当预测变量的数量与样本大小发散到无穷大。我们通过数值模拟和真实的数据分析证明了我们的程序的性能。
ABSTRACT Penalised likelihood methods have been a success in analysing high dimensional data. Tang and Leng [(2010), ‘Penalized High-Dimensional Empirical Likelihood’, Biometrika, 97(4), 905–920] extended the penalisation approach to the empirical likelihood scenario and showed that the penalised empirical likelihood estimator could identify the true predictors consistently in the linear regression models. However, this desired selection consistency property of the penalised empirical likelihood method relies heavily on the choice of the tuning parameter. In this work, we propose a tuning parameter selection procedure for penalised empirical likelihood to guarantee that this selection consistency can be achieved. Specifically, we propose a generalised information criterion (GIC) for the penalised empirical likelihood in the linear regression case. We show that the tuning parameter selected by the GIC yields the true model consistently even when the number of predictors diverges to infinity with the sample size. We demonstrate the performance of our procedure by numerical simulations and a real data analysis.