Online Debiasing for Adaptively Collected High-Dimensional Data With Applications to Time Series Analysis

• 成果类型: Article
• 署名作者: Deshpande, Yash; Javanmard, Adel; Mehrabi, Mohammad
• 署名单位: Massachusetts Institute of Technology (MIT); University of Southern California
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1979011
• 发表日期: 2023
• 页码: 1126-1139
• 关键词: confidence-intervals; regression; DESIGN; therapy; models

摘要

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 theta(0) has sparsity of order o(root n/log p). In this regime, the debiased estimator can be used to compute p-values and confidence intervals of optimal size.