Abstract: 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.

Key words and phrases: Corrected score, functional measurement error, functional principle component, physical activity, quantile regression, wearable devices.