Drawing inferences for high-dimensional linear models: A selection-assisted partial regression and smoothing approach
Drawing inferences for high-dimensional linear models: A selection-assisted partial regression and smoothing approach
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DOI：
10.1111/biom.13013
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发表时间：
2019-06-01
期刊：
影响因子：
1.9
通讯作者：
Li, Yi
中科院分区：
文献类型：
--
作者：
Fei, Zhe;Zhu, Ji;Li, Yi
对高维模型进行推论具有挑战性，因为常规渐近理论不适用。本文提出了一种高维线性模型同时估计和推理的新框架。通过基于给定变量选择方案平滑部分回归估计，我们将问题简化为低维最小二乘估计。该过程称为选择辅助部分回归和平滑 (SPARES)，利用数据分割以及变量选择和部分回归。我们证明 SPARES 估计量是渐近无偏且正态的，并通过非参数 delta 方法导出其方差。该程序的实用性在各种模拟场景下进行评估，并通过与主要竞争对手去偏 LASSO 估计器进行比较。我们应用该方法分析两个基因组数据集并获得具有生物学意义的结果。
Drawing inferences for high-dimensional models is challenging as regular asymptotic theories are not applicable. This article proposes a new framework of simultaneous estimation and inferences for high-dimensional linear models. By smoothing over partial regression estimates based on a given variable selection scheme, we reduce the problem to low-dimensional least squares estimations. The procedure, termed as Selection-assisted Partial Regression and Smoothing (SPARES), utilizes data splitting along with variable selection and partial regression. We show that the SPARES estimator is asymptotically unbiased and normal, and derive its variance via a nonparametric delta method. The utility of the procedure is evaluated under various simulation scenarios and via comparisons with the de-biased LASSO estimators, a major competitor. We apply the method to analyze two genomic datasets and obtain biologically meaningful results.