In this paper, we propose variable selection and estimation in generalized linear models using the seamless (SELO) penalized likelihood approach. The SELO penalty is a smooth function that very closely resembles the discontinuous penalty. We develop an efficient algorithm to fit the model, and show that the SELO‐GLM procedure has the oracle property in the presence of a diverging number of variables. We propose a Bayesian information criterion (BIC) to select the tuning parameter. We show that under some regularity conditions, the proposed SELO‐GLM/BIC procedure consistently selects the true model. We perform simulation studies to evaluate the finite sample performance of the proposed methods. Our simulation studies show that the proposed SELO‐GLM procedure has a better finite sample performance than several existing methods, especially when the number of variables is large and the signals are weak. We apply the SELO‐GLM to analyze a breast cancer genetic dataset to identify the SNPs that are associated with breast cancer risk. The Canadian Journal of Statistics 40: 745–769; 2012 © 2012 Statistical Society of Canada

中文翻译：

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具有无缝 L0 惩罚的广义线性模型中的变量选择和估计。

在本文中，我们使用无缝（SELO）惩罚似然方法在广义线性模型中提出变量选择和估计。SELO 惩罚是一个非常类似于不连续函数的平滑函数惩罚。我们开发了一种有效的算法来拟合模型，并表明 SELO-GLM 过程在存在不同数量的变量时具有预言机属性。我们提出了贝叶斯信息准则（BIC）来选择调整参数。我们表明，在某些规律性条件下，所提出的 SELO-GLM/BIC 程序始终如一地选择真实模型。我们进行模拟研究以评估所提出方法的有限样本性能。我们的模拟研究表明，所提出的 SELO-GLM 程序比几种现有方法具有更好的有限样本性能，尤其是在变量数量较多且信号较弱的情况下。我们应用 SELO-GLM 来分析乳腺癌遗传数据集，以确定与乳腺癌风险相关的 SNP。加拿大统计杂志40：745-769；2012 © 2012 加拿大统计学会