Unconditional Quantile Regression for Streaming Datasets

The Unconditional Quantile Regression (UQR) method, initially introduced by Firpo et al. (2009), has gained significant traction as a popular approach for modeling and analyzing data. However, much like Conditional Quantile Regression (CQR), UQR encounters computational challenges when it comes to obtaining parameter estimates for streaming data sets. This is attributed to the involvement of unknown parameters in the logistic regression loss function utilized in UQR, which presents obstacles in both computational execution and theoretical development. To address this, we present a novel approach involving smoothing logistic regression estimation. Subsequently, we propose a renewable estimator tailored for UQR with streaming data, relying exclusively on current data and summary statistics derived from historical data. Theoretically, our proposed estimators exhibit equivalent asymptotic properties to the standard version computed directly on the entire dataset, without any additional constraints. Both simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed methods.