Large-scale quantile regression with covariates missing at random

Large-scale data has become increasingly prevalent across various domains due to modern technological advancements. Analyzing this extremely large volume of data is inherently complex, as it often exhibits high skewness, heteroscedasticity of variance, and missing values. Quantile regression (QR) is a popular method for analyzing heterogeneous data. In this article, we fit a linear quantile regression model for large-scale data with randomly missing covariates. We integrate information from multiple machines by constructing a communication-efficient surrogate loss (CSL) function. This function combines a weighting method to address missing data with a convolution-type smoothing procedure to deal with the non-smooth quantile regression loss function. Under mild conditions, our proposed estimator demonstrates consistency and asymptotic normality. The proposed approach is evaluated through extensive simulation studies and applied to the Survey data from the Behavioral Risk Factor Surveillance System (BRFSS).