Variable selection in semiparametric regression modeling
Variable selection in semiparametric regression modeling
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DOI：
10.1214/009053607000000604
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发表时间：
2008-02-01
影响因子：
4.5
通讯作者：
Liang, Hua
中科院分区：
文献类型：
--
作者：
Li, Runze;Liang, Hua
本文讨论了半参数模型中重要变量的选取问题。半参数回归模型的变量选择由两部分组成：非参数部分的模型选择和参数部分的显著变量选择。因此，半参数变量选择比参数变量选择更具挑战性（例如，线性和广义线性模型），因为包括逐步回归和最佳子集选择的传统变量选择程序现在需要为每个子模型的非参数分量进行单独的模型选择。这导致非常沉重的计算负担。本文提出了一类利用非凹惩罚似然的半参数回归模型的变量选择方法。我们建立了由此产生的估计的收敛速度。通过适当地选择罚函数和正则化参数，我们证明了所得估计的渐近正态性，并进一步证明了所提出的方法和Oracle方法一样有效。提出了一种半参数广义似然比检验来选择非参数分量中的显著变量。我们研究了所提出的测试的渐近行为，并证明其极限零分布如下卡方分布，这是独立的滋扰参数。进行了广泛的蒙特卡罗模拟研究，以检查有限样本的性能，建议的变量选择程序。
In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for the parametric portion. Thus, semiparametric variable selection is much more challenging than parametric variable selection (e.g., linear and generalized linear models) because traditional variable selection procedures including stepwise regression and the best subset selection now require separate model selection for the nonparametric components for each submodel. This leads to a very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. We establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we show the asymptotic normality of the resulting estimate and further demonstrate that the proposed procedures perform as well as an oracle procedure. A semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a chi-square distribution which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.