<p>Streaming data, characterized by its dynamic nature and real-time continuous flow, has recently garnered significant attention in the field of statistics. Traditional offline methods, designed for static data, are now unsuitable for analyzing these data streams. In this paper, we explore the statistical inference problem for the single-index model with high-dimensional streaming data. We first investigate the penalized estimation of the regression model, deriving error bounds for the online Lasso estimator under regularity conditions. Recognizing the inherent bias in penalized estimators, we propose an online debiased Lasso estimator to enable valid statistical inference. Confidence intervals for individual coefficients are constructed based on the established asymptotic normality. Importantly, our procedures do not impose moment conditions on the error term, making them robust to heavy-tailed distributions and the presence of outliers. We demonstrate the finite sample performance of our proposed method through comprehensive simulation studies and an application to a Nasdaq stock dataset.</p>