GRID:一种高维非参数回归的变量选择和结构发现方法

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
F. Giordano, S. Lahiri, M. L. Parrella
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引用次数: 4

摘要

我们考虑高维的非参数回归,其中只有大量变量中相对较小的子集是相关的,并且可能对响应产生非线性影响。我们开发了变量选择、结构发现和真实低维回归函数估计的方法,允许相关变量之间的任何程度的相互作用,而无需事先指定。所提出的方法称为GRID,以一种新颖的方式将基于经验似然的边际检验与局部线性估计机制相结合,以选择相关变量。此外,它提供了一个简单的图形工具,用于识别回归函数的低维非线性结构。理论结果建立了变量选择和结构发现的一致性以及回归函数的GRID估计量的Oracle风险性质,对于任意a∈(0,∞),允许协变量的维数d以d=O(n)的速率随样本量n增长,并且对于某些γ∈(0,1),允许相关协变量的数量r以r=O(n。在一个中等规模的模拟研究中,研究了网格的有限样本特性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
GRID: A variable selection and structure discovery method for high dimensional nonparametric regression
We consider nonparametric regression in high dimensions where only a relatively small subset of a large number of variables are relevant and may have nonlinear effects on the response. We develop methods for variable selection, structure discovery and estimation of the true low-dimensional regression function, allowing any degree of interactions among the relevant variables that need not be specified a-priori. The proposed method, called the GRID, combines empirical likelihood based marginal testing with the local linear estimation machinery in a novel way to select the relevant variables. Further, it provides a simple graphical tool for identifying the low dimensional nonlinear structure of the regression function. Theoretical results establish consistency of variable selection and structure discovery, and also Oracle risk property of the GRID estimator of the regression function, allowing the dimension d of the covariates to grow with the sample size n at the rate d = O(n) for any a ∈ (0,∞) and the number of relevant covariates r to grow at a rate r = O(n) for some γ ∈ (0, 1) under some regularity conditions that, in particular, require finiteness of certain absolute moments of the error variables depending on a. Finite sample properties of the GRID are investigated in a moderately large simulation study.
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来源期刊
CiteScore
7.20
自引率
4.30%
发文量
567
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