Quantile regression provides a consistent approach to investigating the association between covariates and various aspects of the distribution of the response beyond the mean. When the regression covariates are measured with errors, measurement error (ME) adjustment steps are needed for valid inference. This is true for both scalar and functional covariates. Here, we propose extending the Bayesian measurement error and Bayesian quantile regression literature to allow for available covariates prone to potential complex measurement errors. Our approach uses the Generalized Asymmetric Laplace (GAL) distribution as a working likelihood. The family of GAL distribution has recently emerged as a more flexible distribution family in the Bayesian quantile regression modeling compared to their Asymmetric Laplace (AL) counterpart. We then compared and contrasted two approaches in our ME-adjusted steps through a battery of simulation scenarios. Finally, we apply our approach to the analysis of an NHANES dataset 2013-2014 to model quantiles of Body mass index (BMI) as a function of minute-level device-based physical activity in a cohort of an adult 50 years and above.

翻译：分位数回归提供了一种稳健的方法来研究协变量与响应变量分布中均值以外的多种特征之间的关联。当回归协变量存在测量误差时，需要进行测量误差调整步骤以获得有效的推断结论，这对于标量协变量和函数型协变量均适用。本文提出将贝叶斯测量误差与贝叶斯分位数回归文献进行扩展，以处理可能面临复杂测量误差的可用协变量。该方法采用广义非对称拉普拉斯分布作为工作似然函数。相较于标准非对称拉普拉斯分布，广义非对称拉普拉斯分布族近年来在贝叶斯分位数回归建模中展现出更强的灵活性。我们通过一系列模拟场景对两种测量误差调整方法进行了比较与对比分析。最后，我们将所提方法应用于2013-2014年美国国家健康与营养调查数据，对50岁及以上成年人群的身体质量指数分位数进行建模，以分钟级设备记录的体力活动数据作为函数型协变量。