Online Debiasing for Adaptively Collected High-dimensional Data with Applications to Time Series Analysis

Understand

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, e.g.