Variable selection for multivariate nonparametric regression models usually involves parameterized approximation for nonparametric functions in the objective function. However, this parameterized approximation often increases the number of parameters significantly, leading to the “curse of dimensionality” and inaccurate estimation. In this paper, we propose a novel and easily implemented approach to do variable selection in nonparametric models without parameterized approximation, enabling selection consistency to be achieved. The proposed method is applied to do variable selection for additive models. A two-stage procedure with selection and adaptive estimation is proposed, and the properties of this method are investigated. This two-stage algorithm is adaptive to the smoothness of the underlying components, and the estimation consistency can reach a parametric rate if the underlying model is really parametric. Simulation studies are conducted to examine the performance of the proposed method. Furthermore, a real data example is analyzed for illustration.

中文翻译：

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非参数变量选择及其在加性模型中的应用

多元非参数回归模型的变量选择通常涉及目标函数中非参数函数的参数化近似。然而，这种参数化近似通常会显着增加参数的数量，导致“维度灾难”和不准确的估计。在本文中，我们提出了一种新颖且易于实现的方法，可以在没有参数化近似的非参数模型中进行变量选择，从而实现选择一致性。所提出的方法被应用于对加性模型进行变量选择。提出了具有选择和自适应估计的两阶段程序，并研究了该方法的性质。这种两阶段算法自适应底层组件的平滑度，如果底层模型确实是参数化的，则估计一致性可以达到参数化率。进行模拟研究以检查所提出方法的性能。此外，还分析了一个真实的数据示例以进行说明。