Quantile regression with multiple proxy variables

Data integration has become increasingly popular owing to the availability of multiple data sources. This study considered quantile regression estimation when a key covariate had multiple proxies across several datasets. In a unified estimation procedure, the proposed method incorporates multiple proxies that have both linear and nonlinear relationships with the unobserved covariates. The proposed approach allows the inference of both the quantile function and unobserved covariates and does not require the quantile function's linearity. Simulation studies have demonstrated that this methodology successfully integrates multiple proxies and reveals quantile relationships for a wide range of nonlinear data. The proposed method is applied to administrative data obtained from the Survey of Household Finances and Living Conditions provided by Statistics Korea, to specify the relationship between assets and salary income in the presence of multiple income records.