使用流数据的高维广义线性模型在线推理。

IF 1 4区 数学 Q3 STATISTICS & PROBABILITY Electronic Journal of Statistics Pub Date : 2023-01-01 Epub Date: 2023-11-28 DOI:10.1214/23-ejs2182
Lan Luo, Ruijian Han, Yuanyuan Lin, Jian Huang
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引用次数: 0

摘要

在本文中,我们针对高维广义线性模型开发了一种流数据在线统计推断方法,用于实时估计和推断。我们提出了一种与流数据的数据收集方案相匹配的在线debiased lasso方法。在线去偏拉索与离线去偏拉索在两个重要方面有所不同。首先,它只使用历史数据的摘要统计来更新回归系数的分量置信区间。其次,在线去偏 lasso 增加了一个项,以纠正在线更新过程中积累的近似误差。我们证明,在广义线性模型中,我们提出的在线去偏估计器是渐近正态的。这一结果为利用流数据进行实时临时统计推断提供了理论基础。为了评估我们提出的在线去偏拉索方法的性能,我们进行了大量的数值实验。这些实验证明了我们算法的有效性,并支持理论结果。此外,我们还用一个高维文本数据集说明了我们的方法的应用。
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Online inference in high-dimensional generalized linear models with streaming data.

In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for realtime estimation and inference. We propose an online debiased lasso method that aligns with the data collection scheme of streaming data. Online debiased lasso differs from offline debiased lasso in two important aspects. First, it updates component-wise confidence intervals of regression coefficients with only summary statistics of the historical data. Second, online debiased lasso adds an additional term to correct approximation errors accumulated throughout the online updating procedure. We show that our proposed online debiased estimators in generalized linear models are 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 our proposed online debiased lasso method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. Furthermore, we illustrate the application of our method with a high-dimensional text dataset.

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来源期刊
Electronic Journal of Statistics
Electronic Journal of Statistics STATISTICS & PROBABILITY-
CiteScore
1.80
自引率
9.10%
发文量
100
审稿时长
3 months
期刊介绍: The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.
期刊最新文献
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