Integrative Quantile Regression Analysis of Heterogeneous Multisource Data with Privacy Preserving

Researchers have used and discussed multisource data integrative analysis in many fields.In this paper, we focus on quantile regression for an analysis that has not been investigated in the literature.Specifically, we consider quantile integrative analysis of multisource and high-dimensional data where both homogeneity and heterogeneity may exist in covariate effects among different data sets.We aim to detect the homogenous and heterogenous effects, obtain the estimators of corresponding parameters, and improve the statistical efficiency of the potential homogeneous covariate effects by integrating the information contained in different data sources, while the raw data are unavailable.For the problem, we propose an objective function based on a composite penalty.In particular, we propose the composite penalty term to pursue the homogeneous and nonzero covariate effects when the dimension of covariates is high; the main term of the objective function can aggregate the quantile regression estimators from the various data sources and hence improve the statistical efficiency of potential homogeneous covariate effects.Meanwhile, it relies only on the summary statistics from each data source and thus can protect privacy to a great extent.