Ignoring measurement errors in conventional regression analyses can lead to biased estimation and inference results. Reducing such bias is challenging when the error-prone covariate is a functional curve. In this paper, we propose a new corrected loss function for a partially functional linear quantile model with function-valued measurement errors. We establish the asymptotic properties of both the functional coefficient and the parametric coefficient estimators. We also demonstrate the finite-sample performance of the proposed method using simulation studies, and illustrate its advantages by applying it to data from a children obesity study.
Keywords: Corrected score; functional measurement error; functional principle component; physical activity; quantile regression; wearable devices.