Homogeneity Pursuit
Homogeneity Pursuit
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DOI：
10.1080/01621459.2014.892882
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发表时间：
2015-03-01
影响因子：
3.7
通讯作者：
Wu, Yichao
中科院分区：
文献类型：
--
作者：
Ke, Zheng Tracy;Fan, Jianqing;Wu, Yichao
本文探讨了高维回归中系数的齐次性，它扩展了稀疏性的概念，更具有一般性，适用于许多应用。当邻近地理区域或类似协变量簇对应的回归系数预计大致相同时，就会出现同质性。稀疏性对应于具有已知原子零的大簇的均匀性的特殊情况。在这篇文章中，我们提出了一种新的方法，称为聚类算法，通过数据驱动的分割（DRDD）回归探索同质性。提供了新的数学增益，可以通过探索均匀性。分析了两个版本的统计特性。特别是，我们提出的估计量的渐近正态性，这表明更好的估计精度齐次参数比没有齐次探索。当我们的方法与稀疏性探索相结合时，可以实现比单独的稀疏性探索更高的效率。这为在高维回归中探索低维结构的能力提供了额外的见解：同质性和稀疏性。我们的研究结果也揭示了融合Lasso的性质。通过对真实的数据的模拟研究和应用，进一步说明了新开发的方法。本文的补充材料可在网上查阅。
This article explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of homogeneity with a large cluster of known atom zero. In this article, we propose a new method called clustering algorithm in regression via data-driven segmentation (CARDS) to explore homogeneity. New mathematics are provided on the gain that can be achieved by exploring homogeneity. Statistical properties of two versions of CARDS are analyzed. In particular, the asymptotic normality of our proposed CARDS estimator is established, which reveals better estimation accuracy for homogeneous parameters than that without homogeneity exploration. When our methods are combined with sparsity exploration, further efficiency can be achieved beyond the exploration of sparsity alone. This provides additional insights into the power of exploring low-dimensional structures in high-dimensional regression: homogeneity and sparsity. Our results also shed lights on the properties of the fused Lasso. The newly developed method is further illustrated by simulation studies and applications to real data. Supplementary materials for this article are available online.