A new estimation in functional linear concurrent model with covariate dependent and noise contamination

Functional linear concurrent regression model is an important model in functional regression. It is usually assumed that realizations of functional covariate are independent and observed precisely. But in practice, the dependence across different functional sample curves often exists. Moreover, each realization of functional covariate may be contaminated with noise. To address this issue, we propose a novel estimation method, which makes full use of dependence information and filters out the impact of measured noise. Then, we extend the proposed method to partially observed functional data. Under some regular conditions, we establish asymptotic properties of the estimators of the model. Finite-sample performance of our estimation is illustrated by Monte Carlo simulation studies and a real data example. Numerical results reveal that the proposed method exhibits superior performance compared with the existing methods.