  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.
