流数据下高维广义线性模型的统计推断
Statistical Inference in High-dimensional Generalized Linear Models with Streaming Data
摘要：
在本文中，我们开发了一个在线的统计推断方法的高维广义线性模型与流数据的实时估计和推理。我们提出了一种在线去偏套索（ODL）方法，以适应特殊的流数据结构。ODL在两个重要方面不同于离线去偏套索。首先，在计算现阶段的估计时，它只使用历史数据的汇总统计。第二，除了去偏在线套索估计，ODL校正的近似误差项所产生的非线性在线更新与流数据。我们证明了所提出的GLM的在线去偏估计是一致的和渐近正态的。这一结果为利用流数据进行实时中间统计推断提供了理论依据。大量的数值实验进行了评估所提出的ODL方法的性能。这些实验证明了我们的算法的有效性和支持的理论结果。通过对美国国家汽车抽样系统-耐撞性数据系统的数据流进行分析，说明了该方法的应用。
英文摘要：
In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for real-time estimation and inference. We propose an online debiased lasso (ODL) method to accommodate the special structure of streaming data. ODL differs from offline debiased lasso in two important aspects. First, in computing the estimate at the current stage, it only uses summary statistics of the historical data. Second, in addition to debiasing an online lasso estimator, ODL corrects an approximation error term arising from nonlinear online updating with streaming data. We show that the proposed online debiased estimators for the GLMs are consistent and asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of the proposed ODL method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. A streaming dataset from the National Automotive Sampling System-Crashworthiness Data System is analyzed to illustrate the application of the proposed method.
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