Wearable devices enable the continuous monitoring of physical activity (PA) but generate complex functional data with poorly characterized errors. Most work on functional data views the data as smooth, latent curves obtained at discrete time intervals with some random noise with mean zero and constant variance. Viewing this noise as homoscedastic and independent ignores potential serial correlations. Our preliminary studies indicate that failing to account for these serial correlations can bias estimations. In dietary assessments, epidemiologists often use self-reported measures based on food frequency questionnaires that are prone to recall bias. With the increased availability of complex, high-dimensional functional, and scalar biomedical data potentially prone to measurement errors, it is necessary to adjust for biases induced by these errors to permit accurate analyses in various regression settings. However, there has been limited work to address measurement errors in functional and scalar covariates in the context of quantile regression. Therefore, we developed new statistical methods based on simulation extrapolation (SIMEX) and mixed effects regression with repeated measures to correct for measurement error biases in this context. We conducted simulation studies to establish the finite sample properties of our new methods. The methods are illustrated through application to a real data set.

翻译：可穿戴设备使物理活动（PA）的持续监测成为可能，但会产生复杂的功能数据且误差特征描述不充分。现有功能数据分析通常将数据视为在离散时间间隔内获取的平滑潜曲线，并假设伴随均值为零、方差恒定的随机噪声。将此类噪声视为同方差且独立会忽略潜在的序列相关性。我们的初步研究表明，未考虑这些序列相关性会导致估计偏差。在膳食评估中，流行病学家常采用基于食物频率问卷的自我报告测量，这类方法易受回忆偏倚影响。随着复杂高维功能数据与标量生物医学数据的可获取性增加——这些数据可能存在测量误差，有必要校正这些误差引发的偏差，以实现在不同回归设定下的精确分析。然而，目前针对分位数回归中功能与标量协变量测量误差问题的研究有限。为此，我们基于模拟外推法（SIMEX）和含重复测量的混合效应回归开发了新的统计方法，以校正该场景下的测量误差偏差。通过模拟研究确立了新方法的有限样本性质，并将方法应用于实际数据集进行验证。