Scalar-on-Function Regression with Replicated Error-Prone Functional Covariates

In this article, we study scalar-on-function regression with functional covariates observed through replicated measurements subject to measurement error. Treating replicated curves as surrogates of an underlying latent process, the proposed framework resolves the identifiability issues commonly encountered in functional measurement error models. Through functional principal component analysis, the model is represented as a finite-dimensional hierarchical linear measurement error model. Parameter estimation is carried out using an expectation-maximization algorithm, and alternative correction strategies based on adjusted regression calibration and simulation extrapolation are also considered for comparison. Simulation studies demonstrate the advantages of explicitly accounting for measurement error in terms of bias reduction and estimation stability. An application to soybean yield prediction in Illinois, using meteorological variables contaminated by measurement error, illustrates the practical value of the proposed approach.