Unconditional Quantile Regression for Streaming Datasets
针对流式数据中无条件分位数回归的计算难题，提出一种基于平滑逻辑回归的可更新估计方法，仅需当前数据和历史摘要统计量，理论证明其渐近性质与全样本估计等价。
The Unconditional Quantile Regression (UQR) method, initially introduced by Firpo et al. 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 datasets. This is attributed to the involvement of unknown parameters in the logistic regression loss function used 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.