Component Identification and Estimation in Nonlinear High-Dimensional Regression Models by Structural Adaptation
Component Identification and Estimation in Nonlinear High-Dimensional Regression Models by Structural Adaptation
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DOI：
10.1198/016214504000001529
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发表时间：
2005-06
影响因子：
3.7
通讯作者：
A. Samarov;V. Spokoiny;C. Vial
中科院分区：
文献类型：
--
作者：
A. Samarov;V. Spokoiny;C. Vial
本文提出了一种分析非线性成分完全未知的部分线性模型的新方法。分析的目标是识别以非线性方式进入模型函数的一组回归量，并完成模型的估计，包括线性分量的斜率系数和非线性分量的链接函数。该程序还允许选择显著的回归变量。我们还开发了一个测试的线性假设对一个部分线性的替代品，或更一般地说，一个测试，非线性组件是M维的M = 0，1，2，...。本文提出的方法对未知的模型结构具有完全的自适应性，并且适用于模型的温和条件。唯一重要的假设是非线性分量的维数相对较小。理论结果表明，该程序提供了一个规定的水平的识别误差和估计的线性分量的精度为n-1/2。数值研究表明，即使是小或中等样本量的方法有很好的性能。
This article proposes a new method of analysis of a partially linear model whose nonlinear component is completely unknown. The target of analysis is identification of the set of regressors that enter in a nonlinear way in the model function, and complete estimation of the model, including slope coefficients of the linear component and the link function of the nonlinear component. The procedure also allows selection of the significant regression variables. We also develop a test of linear hypothesis against a partially linear alternative or, more generally, a test that the nonlinear component is M-dimensional for M = 0, 1, 2,…. The approach proposed in this article is fully adaptive to the unknown model structure and applies under mild conditions on the model. The only important assumption is that the dimensionality of nonlinear component is relatively small. The theoretical results indicate that the procedure provides a prescribed level of the identification error and estimates the linear component with accuracy of order n−1/2. A numerical study demonstrates a very good performance of the method for even small or moderate sample sizes.