  Traditional statistical methods are faced with new challenges due to
streaming data. The major challenge is the rapidly growing volume and velocity
of data, which makes storing such huge datasets in memory impossible. The paper
presents an online inference framework for regression parameters in
high-dimensional semiparametric single-index models with unknown link
functions. The proposed online procedure updates only the current data batch
and summary statistics of historical data instead of re-accessing the entire
raw data set. At the same time, we do not need to estimate the unknown link
function, which is a highly challenging task. In addition, a generalized convex
loss function is used in the proposed inference procedure. To illustrate the
proposed method, we use the Huber loss function and the logistic regression
model's negative log-likelihood. In this study, the asymptotic normality of the
proposed online debiased Lasso estimators and the bounds of the proposed online
Lasso estimators are investigated. To evaluate the performance of the proposed
method, extensive simulation studies have been conducted. We provide
applications to Nasdaq stock prices and financial distress datasets.
