Model selection for high dimensional nonparametric additive models via ridge estimation
Model selection for high dimensional nonparametric additive models via ridge estimation
复制标题
通过岭估计选择高维非参数加性模型的模型
DOI：
10.3390/math10234551
复制
发表时间：
2022
期刊：
影响因子：
2.4
通讯作者：
Jiang Xuejun
中科院分区：
文献类型：
--
作者：
Wang Haofeng;Jin Hongxia;Jiang Xuejun
在超高维数据分析中，为了保持良好的计算性能和良好的统计特性，非参数加性模型面临着越来越大的挑战。为了克服这些问题，我们引入了一种高维非参数加性模型的模型选择方法。我们的方法是提出一种新的群体筛选程序，通过非参数平滑脊估计（GRIE）来找到每个协变量的重要性。然后结合GRIE的确定筛选特性和扩展贝叶斯信息准则（EBIC）的模型选择特性，在非参数加性模型中选择合适的子模型。从理论上讲，我们为所提出的方法建立了模型选择的强一致性。大量的仿真和两个真实数据集证明了GRIE-EBIC方法的卓越性能。
In ultrahigh dimensional data analysis, to keep computational performance well and good statistical properties still working, nonparametric additive models face increasing challenges. To overcome them, we introduce a methodology of model selection for high dimensional nonparametric additive models. Our approach is to propose a novel group screening procedure via nonparametric smoothing ridge estimation (GRIE) to find the importance of each covariate. It is then combined with the sure screening property of GRIE and the model selection property of extended Bayesian information criteria (EBIC) to select the suitable sub-models in nonparametric additive models. Theoretically, we establish the strong consistency of model selection for the proposed method. Extensive simulations and two real datasets illustrate the outstanding performance of the GRIE-EBIC method.