Online Debiasing for Adaptively Collected High-Dimensional Data With Applications to Time Series Analysis
Online Debiasing for Adaptively Collected High-Dimensional Data With Applications to Time Series Analysis
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DOI：
10.1080/01621459.2021.1979011
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发表时间：
2019-11
影响因子：
3.7
通讯作者：
Y. Deshpande;Adel Javanmard;M. Mehrabi
中科院分区：
文献类型：
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作者：
Y. Deshpande;Adel Javanmard;M. Mehrabi
摘要自适应数据收集在科学和工程应用中是常见的。然而，从统计推断的角度来看，自适应数据收集导致样本中的记忆和相关性，并提出了重大挑战。我们考虑高维线性回归，其中样本是自适应收集的，样本大小n可以小于协变量的数量p。在这种情况下，有两个不同的偏差来源：第一个是由于一致估计所施加的正则化，例如使用LASSO，第二个是由于收集样本的自适应性。我们提出了“在线去偏”，一个通用的程序估计，如LASSO，它解决了两个来源的偏见。在两个具体的情况下（i）时间序列分析和（ii）批量数据收集，我们证明了在线去偏最佳的LASSO估计时，底层参数θ 0的顺序稀疏。在这种情况下，去偏估计量可用于计算最佳大小的p值和置信区间。
Abstract Adaptive collection of data is commonplace in applications throughout science and engineering. From the point of view of statistical inference, however, adaptive data collection induces memory and correlation in the samples, and poses significant challenge. We consider the high-dimensional linear regression, where the samples are collected adaptively, and the sample size n can be smaller than p, the number of covariates. In this setting, there are two distinct sources of bias: the first due to regularization imposed for consistent estimation, for example, using the LASSO, and the second due to adaptivity in collecting the samples. We propose “online debiasing,” a general procedure for estimators such as the LASSO, which addresses both sources of bias. In two concrete contexts (i) time series analysis and (ii) batched data collection, we demonstrate that online debiasing optimally debiases the LASSO estimate when the underlying parameter θ 0 has sparsity of order . In this regime, the debiased estimator can be used to compute p-values and confidence intervals of optimal size.