Robustness of SIMEX to non-normal measurement error

Investigate whether the simulation-extrapolation (SIMEX) estimator for scalar-on-function regression remains robust when the functional measurement errors are non-normal.

Background

The proposed SIMEX methodology is developed primarily under normal measurement-error assumptions, including independent Gaussian errors in the functional regressors. The discussion identifies robustness to departures from normality as an unresolved methodological issue requiring further investigation. Establishing such robustness would clarify whether SIMEX remains reliable for functional data with non-Gaussian measurement-error distributions.