Data integration has become more challenging with the emerging availability of multiple data sources. This paper considers Bayesian quantile regression estimation when the key covariate is not directly observed, but the unobserved covariate has multiple proxies. In a unified estimation procedure, the proposed method incorporates these multiple proxies, which have various relationships with the unobserved covariate. The proposed approach allows the inference of both the quantile function and unobserved covariate. Moreover, it requires no linearity of the quantile function or parametric assumptions on the regression error distribution and simultaneously accommodates both linear and nonlinear proxies. The simulation studies show that this methodology successfully integrates multiple proxies and reveals the quantile relationship for a wide range of nonlinear data. The proposed method is applied to the administrative data obtained from the Survey of Household Finances and Living Conditions provided by Statistics Korea. The proposed Bayesian quantile regression is implemented to specify the relationship between assets and salary income in the presence of multiple income records.
翻译:随着多种数据源的出现,数据整合变得更具挑战性。本文认为,当关键共变项未直接观测到,但未观测到的共变项有多个替代物时,巴伊西亚四分位回归估计会比较具有挑战性。在一个统一的估算程序中,拟议方法将这些与未观测的共变项有不同关系的多个代理物纳入其中。拟议方法允许量化函数和未观测到的共变项的推论。此外,在回归错误分布上,不要求量化函数或参数假设的直线性和非线性替代物的直线性或非线性替代物的直线性。模拟研究表明,这一方法成功地整合了多个代理物,并揭示了广泛的非线性数据的四分位关系。拟议方法适用于韩国统计局提供的家庭财务和生活状况调查的行政数据。拟议贝伊斯四分位回归是为了具体说明多重收入记录中的资产与工资收入之间的关系。