Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach
Estimation and Inference for High Dimensional Generalized Linear Models: A Splitting and Smoothing Approach
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发表时间：
2019-03
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通讯作者：
Z. Fei;Yi Li
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作者：
Z. Fei;Yi Li
现代生物医学研究的重点已逐渐转向解释和估计高维预测因子对疾病风险的联合影响。量化这些估计中的不确定性可能为患者和医生提供对预防策略或治疗决策的有价值的见解。高维推理，包括可信区间和假设检验，引起了人们的极大兴趣。虽然在线性回归环境下已经做了大量的工作，但关于高维广义线性模型的推断的文献还很少。我们提出了一种新颖且在计算上可行的方法，该方法适用于多种结果类型，包括正态数据、二项数据和泊松数据。我们使用“分裂和平滑”的方法，将样本分成两部分，其中一部分进行变量选择，另一部分进行偏回归。对多个随机分裂的估计进行平均，我们得到了数值稳定的平滑估计。我们证明了估计是一致的、渐近正态的，并构造了具有适当覆盖概率的所有预报器的置信度区间。我们通过与现有方法的比较来检验我们方法的有限样本性能，并将其应用于分析一项肺癌队列研究。
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into prevention strategies or treatment decisions for both patients and physicians. High dimensional inference, including confidence intervals and hypothesis testing, has sparked much interest. While much work has been done in the linear regression setting, there is lack of literature on inference for high dimensional generalized linear models. We propose a novel and computationally feasible method, which accommodates a variety of outcome types, including normal, binomial, and Poisson data. We use a “splitting and smoothing” approach, which splits samples into two parts, performs variable selection using one part and conducts partial regression with the other part. Averaging the estimates over multiple random splits, we obtain the smoothed estimates, which are numerically stable. We show that the estimates are consistent, asymptotically normal, and construct confidence intervals with proper coverage probabilities for all predictors. We examine the finite sample performance of our method by comparing it with the existing methods and applying it to analyze a lung cancer cohort study.