  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 various relationships with the unobserved covariates. The proposed
approach allows the inference of both the quantile function and unobserved
covariates. Moreover, it does not require the quantile function's linearity
and, simultaneously, accommodates both the linear and nonlinear proxies.
Simulation studies have demonstrated that this methodology successfully
integrates multiple proxies and revealed 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.
