Errors-in-variables regression for mixed Euclidean and non-Euclidean predictors

In this paper, we explore a novel regression problem encompassing both Euclidean and non-Euclidean predictors, all of which are subject to measurement errors. Specifically, we focus on a non-Euclidean predictor taking values in a compact and connected Lie group. We propose a nonparametric estimator and establish its asymptotic properties, including rates of convergence and an asymptotic distribution. We validate the practical efficacy of our estimator through simulation studies and real data analysis.