首页|非参数可加模型的迭代自适应稳健变量选择

非参数可加模型的迭代自适应稳健变量选择

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  • 维普
本文结合稳健损失函数、B样条逼近和自适应组Lasso研究一个高维可加模型,以识别"大p小n"下的不显著协变量.与传统的最小二乘自适应组Lasso相比,该方法具有较好的抵消重尾误差和异常值的影响.为证明方便,本文进一步考虑了更一般的加权稳健组Lasso估计,且该权向量对所建议的估计量具有模型选择oracle性质和渐近正态性的证明中起着关键作用.稳健组Lasso和自适应稳健组Lasso可以看作是加权稳健组Lasso在不同权向量下的特殊情况.在实际应用中,我们使用稳健组Lasso获得初始估计以降低问题的维数,然后使用迭代自适应稳健组Lasso选择非零分量.数值结果表明,所提出的方法对中等规模的样本具有良好的适用性.高维基因TRIM32数据验证了该方法的应用.
Iterative Adaptive Robust Variable Selection in Nomparametric Additive Models
By utilizing the robust loss function,B-spline approximation and adaptive group Las-so,a nonparametric additive model is investigated to identify insignificant covariates for the"large p small n"setting.Compared with the ordinary least-square adaptive group Lasso,the proposed method is resistant to heavy-tailed errors or outlines in the responses.To prove facilitate presen-tation,a more general weighted robust group Lasso estimator is considered.Moreover,the weight vectors play a pivotal role for the suggested estimators to enjoy the model selection oracle property and asymptotic normality.The robust group Lasso and adaptive robust group Lasso can be seen as special circumstances of different weight vectors.In practice,we use the robust group Lasso to obtain an initial estimator to reduce the dimension of the problem,and then apply the iterative adaptive robust group Lasso to select nonzero components.The results of simulation studies show that the proposed methods work well with samples of moderate size.A high-dimensional gene TRIM32 data is used to illustrate the application of the proposed method.

adaptive group Lassohigh-dimensional datanonparametric regressionoracle prop-ertyrobust estimation

朱能辉、尤进红、徐群芳

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厦门理工学院数学与统计学院,厦门,361024

上海财经大学统计与管理学院,上海,200433

宁波大学商学院,宁波,315211

自适应组Lasso 高维数据 非参数回归 oracle性质 稳健估计

国家自然科学基金国家社会科学基金Fujian Alliance of MathematicsScientific Research Climbing Program of Xiamen University of Tech-nology

1197129119BTJ0322023SXLMMS10XPDKT20037

2024

10.3969/j.issn.1001-4268.2024.02.001

应用概率统计
中国数学会概率统计学会

应用概率统计

CSTPCD北大核心
影响因子：0.263
ISSN：1001-4268
年,卷(期)：2024.40(2)
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