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Consistent Fixed-Effects Selection in Ultra-high dimensional Linear Mixed Models with Error-Covariate Endogeneity
Statistica Sinica ( IF 1.5 ) Pub Date : 2021-01-01 , DOI: 10.5705/ss.202019.0421
Abhik Ghosh , Magne Thoresen

Recently, applied sciences, including longitudinal and clustered studies in biomedicine require the analysis of ultra-high dimensional linear mixed effects models where we need to select important fixed effect variables from a vast pool of available candidates. However, all existing literature assume that all the available covariates and random effect components are independent of the model error which is often violated (endogeneity) in practice. In this paper, we first investigate this important issue in ultra-high dimensional linear mixed effects models with particular focus on the fixed effects selection. We study the effects of different types of endogeneity on existing regularization methods and prove their inconsistencies. Then, we propose a new profiled focused generalized method of moments (PFGMM) approach to consistently select fixed effects under 'error-covariate' endogeneity, i.e., in the presence of correlation between the model error and covariates. Our proposal is proved to be oracle consistent with probability tending to one and works well under most other type of endogeneity too. Additionally, we also propose and illustrate a few consistent parameter estimators, including those of the variance components, along with variable selection through PFGMM. Empirical simulations and an interesting real data example further support the claimed utility of our proposal.

中文翻译:

具有误差协变量内生性的超高维线性混合模型中的一致固定效应选择

最近,应用科学,包括生物医学的纵向和集群研究,需要分析超高维线性混合效应模型,我们需要从大量可用的候选变量中选择重要的固定效应变量。然而,所有现有文献都假设所有可用的协变量和随机效应分量都与模型误差无关,而模型误差在实践中经常被违反(内生性)。在本文中,我们首先研究了超高维线性混合效应模型中的这个重要问题,特别关注固定效应的选择。我们研究了不同类型的内生性对现有正则化方法的影响并证明了它们的不一致性。然后,我们提出了一种新的轮廓聚焦广义矩方法 (PFGMM) 方法,以在“误差-协变量”内生性下一致地选择固定效应,即在模型误差和协变量之间存在相关性的情况下。我们的提议被证明是与趋向于 1 的概率一致的预言机,并且在大多数其他类型的内生性下也能很好地工作。此外,我们还提出并说明了一些一致的参数估计器,包括方差分量的估计器,以及通过 PFGMM 进行的变量选择。实证模拟和一个有趣的真实数据示例进一步支持了我们的提议所声称的效用。我们的提议被证明是与趋向于 1 的概率一致的预言机,并且在大多数其他类型的内生性下也能很好地工作。此外,我们还提出并说明了一些一致的参数估计器,包括方差分量的估计器,以及通过 PFGMM 进行的变量选择。实证模拟和一个有趣的真实数据示例进一步支持了我们的提议所声称的效用。我们的提议被证明是与趋向于 1 的概率一致的预言机,并且在大多数其他类型的内生性下也能很好地工作。此外,我们还提出并说明了一些一致的参数估计器,包括方差分量的估计器,以及通过 PFGMM 进行的变量选择。实证模拟和一个有趣的真实数据示例进一步支持了我们的提议所声称的效用。
更新日期:2021-01-01
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