具有协变量测量误差的多元回归模型中的变量选择

IF 1.4 3区 数学 Q2 STATISTICS & PROBABILITY
Jingyu Cui , Grace Y. Yi
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引用次数: 0

摘要

多变量回归模型被广泛用于分析具有多维响应变量的数据。然而,测量误差和虚假变量的存在阻碍了此类模型的使用。虽然具有这些特征的数据在应用中很常见,但有关这些特征的研究却很少。在本文中,我们考虑了具有测量误差协变量的多元回归模型下的变量选择问题。为了获得灵活性,我们允许协变量和响应变量的维度是固定的,或者随着样本量的增加而发散。我们提出了一种新的正则化方法来处理误差污染数据的变量选择和测量误差效应。我们提出的惩罚偏差校正最小二乘法可以灵活地从一类具有不同特征的函数中选择惩罚函数。重要的是,我们的方法不需要相关变量的完全分布假设,从而扩大了其适用范围。我们为所提出的方法建立了严谨的理论结果,并描述了计算效率高的程序。数值研究证实了所提方法在有限设置下的令人满意的性能,同时也证明了在推断程序中忽略测量误差的有害影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Variable selection in multivariate regression models with measurement error in covariates

Multivariate regression models have been broadly used in analyzing data having multi-dimensional response variables. The use of such models is, however, impeded by the presence of measurement error and spurious variables. While data with such features are common in applications, there has been little work available concerning these features jointly. In this article, we consider variable selection under multivariate regression models with covariates subject to measurement error. To gain flexibility, we allow the dimensions of the covariate and response variables to be either fixed or diverging as the sample size increases. A new regularized method is proposed to handle both variable selection and measurement error effects for error-contaminated data. Our proposed penalized bias-corrected least squares method offers flexibility in selecting the penalty function from a class of functions with different features. Importantly, our method does not require full distributional assumptions for the associated variables, thereby broadening its applicability. We rigorously establish theoretical results and describe a computationally efficient procedure for the proposed method. Numerical studies confirm the satisfactory performance of the proposed method under finite settings, and also demonstrate deleterious effects of ignoring measurement error in inferential procedures.

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来源期刊
Journal of Multivariate Analysis
Journal of Multivariate Analysis 数学-统计学与概率论
CiteScore
2.40
自引率
25.00%
发文量
108
审稿时长
74 days
期刊介绍: Founded in 1971, the Journal of Multivariate Analysis (JMVA) is the central venue for the publication of new, relevant methodology and particularly innovative applications pertaining to the analysis and interpretation of multidimensional data. The journal welcomes contributions to all aspects of multivariate data analysis and modeling, including cluster analysis, discriminant analysis, factor analysis, and multidimensional continuous or discrete distribution theory. Topics of current interest include, but are not limited to, inferential aspects of Copula modeling Functional data analysis Graphical modeling High-dimensional data analysis Image analysis Multivariate extreme-value theory Sparse modeling Spatial statistics.
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